In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

In this paper, we consider the classic fair division problem of allocating m divisible items to n agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of n and m. In particular, we show a tight approximation bound of Θ(√n) for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of O(m^(2/3)) for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multidimensional information sets.

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters that are cohesive in that close by pairs of nodes are assigned to the same cluster with high probability. We consider the additional aspect of individual fairness – pairs of nodes at comparable distances should be separated with comparable probability. We show that classic decomposition procedures do not satisfy this property. We present novel algorithms that achieve various trade-offs between this property and additional desiderata of connectivity of the clusters and optimality in number of clusters. We show that our individual fairness bounds may be difficult to improve by tying the improvement to resolving a major open question in metric embeddings. We finally show the efficacy of our algorithms on real planar networks modeling Congressional redistricting.

A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize functions of buyers’ welfare that reward more balanced surplus allocations.

This paper explores the design of a balanced data-sharing marketplace for entities with heterogeneous datasets and machine learning models that they seek to refine using data from other agents. The goal of the marketplace is to encourage participation for data sharing in the presence of such heterogeneity. Our market design approach for data sharing focuses on interim utility balance, where participants contribute and receive equitable utility from refinement of their models. We present such a market model for which we study computational complexity, solution existence, and approximation algorithms for welfare maximization and core stability. We finally support our theoretical insights with simulations on a mean estimation task inspired by road traffic delay estimation.

For many of the classic online learning settings, it is known that having a “hint” about the loss function before making a prediction yields significantly better regret guarantees. In this work we study the question, do hints allow us to go beyond the standard notion of regret (which competes against the best fixed strategy) and compete against adaptive or dynamic strategies? After all, if hints were perfect, we can clearly compete against a fully dynamic strategy. For some common online learning settings, we provide upper and lower bounds for the switching regret, i.e., the difference between the loss incurred by the algorithm and the optimal strategy in hindsight that switches state at most $L$ times, where $L$ is some parameter. We show positive results for online linear optimization and the classic experts problem. Interestingly, such results turn out to be impossible for the classic bandit setting.

We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number ($k$) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with $k=2$ suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochastic MAB with independent arms from $O(\sqrt{nT})$ to $O(n^2 \log T)$, where $n$ is the number of arms and $T$ is the horizon length. For stochastic MAB, we also consider a stronger model where a probe reveals the reward values of the probed arms, and show that in this case, $k=3$ probes suffice to achieve parameter-independent constant regret, $O(n^2)$. Such regret bounds cannot be achieved even with full feedback after the play, showcasing the power of limited ``advice'' via probing before making the play. We also present extensions to the setting where the hints can be imperfect, and to the case of stochastic MAB where the rewards of the arms can be correlated.

We consider the classical multiwinner election problem where the goal is to choose a subset of k unit-sized candidates (called committee) given utility functions of the voters. We allow arbitrary additional constraints on the chosen committee, and the utilities of voters to belong to a very general class of set functions called β-self bounding. When β = 1, this class includes XOS (and hence, submodular and additive) utilities as special cases. We define a novel generalization of core stability called restrained core to handle constraints on the committee, and consider multiplicative approximations on the utility under this notion.

We model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition P of the plane into regions so that each region contains roughly s = n/k points. P should satisfy a notion of "local" fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in P if it belongs to the minority party. A group D of roughly s contiguous points is called a deviating group with respect to P if majority of points in D are unhappy in P. The partition P is locally fair if there is no deviating group with respect to P. This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and "beyond worst-case" settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are "runs" of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of s, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomial-time algorithm for computing a locally fair partition if one exists.

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of the same interest and in the minority of their respective districts; such a set of individuals have a justified complaint with how the redistricting plan was drawn. A redistricting plan with no deviating groups is called locally fair. We show that the problem of auditing a given plan for local fairness is NP-complete. We present an MCMC approach for auditing as well as ranking redistricting plans. We also present a dynamic programming based algorithm for the auditing problem that we use to demonstrate the efficacy of our MCMC approach. Using these tools, we test local fairness on real-world election data, showing that it is indeed possible to find plans that are almost or exactly locally fair. Further, we show that such plans can be generated while sacrificing very little in terms of compactness and existing fairness measures such as competitiveness of the districts or seat shares of the plans.

We study the limits of an information intermediary in the classical Bayesian auction, where a revenue-maximizing seller sells one item to n buyers with independent private values. In addition, we have an intermediary who knows the buyers' private values, and can map these to a public signal so as to increase consumer surplus. This model generalizes the single-buyer setting proposed by Bergemann, Brooks, and Morris, who present a signaling scheme that raises the optimal consumer surplus, by guaranteeing that the item is always sold and the seller gets the same revenue as without signaling. Our work aims to understand how this result ports to the setting with multiple buyers.

We study the power of price discrimination via an intermediary in bilateral trade, when there is a revenue-maximizing seller selling an item to a buyer with a private value drawn from a prior. Between the seller and the buyer, there is an intermediary that can segment the market by releasing information about the true values to the seller. This is termed signaling, and enables the seller to price discriminate. In this setting, Bergemann et al. showed the existence of a signaling scheme that simultaneously raises the optimal consumer surplus, guarantees the item always sells, and ensures the seller's revenue does not increase.

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an α factor. If no blocking committee exists under this definition, we call this an α-core. Our main result is that an α-core, for α < 67.37, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to α < 9.27 for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of α > 1.015 for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

Standard approaches to group-based notions of fairness, such as parity and equalized odds, try to equalize absolute measures of performance across known groups (based on race, gender, etc.). Consequently, a group that is inherently harder to classify may hold back the performance on other groups; and no guarantees can be provided for unforeseen groups. Instead, we propose a fairness notion whose guarantee, on each group $g$ in a class $\mathcal{G}$, is relative to the performance of the best classifier on $g$. We apply this notion to broad classes of groups, in particular, where (a) $\mathcal{G}$ consists of all possible groups (subsets) in the data, and (b) $\mathcal{G}$ is more streamlined. For the first setting, which is akin to groups being completely unknown, we devise the PF (Proportional Fairness) classifier, which guarantees, on any possible group $g$, an accuracy that is proportional to that of the optimal classifier for $g$, scaled by the relative size of $g$ in the data set. Due to including all possible groups, some of which could be too complex to be relevant, the worst-case theoretical guarantees here have to be proportionally weaker for smaller subsets. For the second setting, we devise the BeFair (Best-effort Fair) framework which seeks an accuracy, on every $g \in \mathcal{G}$, which approximates that of the optimal classifier on $g$, independent of the size of $g$. Aiming for such a guarantee results in a non-convex problem, and we design novel techniques to get around this difficulty when $\mathcal{G}$ is the set of linear hypotheses. We test our algorithms on real-world data sets, and present interesting comparative insights on their performance.

We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce {\emph diversity constraints} on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity. We codify this via two desiderata capturing {\em robustness}. These are {\emph no negative externality} -- other agents are not hurt -- and {\emph monotonicity} -- the agent enforcing the constraint does not see a large increase in value. We show in a formal sense that the Nash Welfare rule that maximizes product of agent values is {\emph uniquely} positioned to be robust when diversity constraints are introduced, while almost all other natural allocation rules fail this criterion. We also show that the guarantees achieved by Nash Welfare are nearly optimal within a widely studied class of allocation rules. We finally perform an empirical simulation on real-world data that models ad allocations to show that this gap between Nash Welfare and other rules persists in the wild.

We consider the algorithmic question of choosing a subset of candidates of a given size k from a set of m candidates, with knowledge of voters' ordinal rankings over all candidates. We consider the well-known and classic scoring rule for achieving diverse representation: the Chamberlin-Courant (CC) or 1-Borda rule, where the score of a committee is the average over the voters, of the rank of the best candidate in the committee for that voter; and its generalization to the average of the top s best candidates, called the s-Borda rule. Our first result is an improved analysis of the natural and well-studied greedy heuristic. We show that greedy achieves a (1 - 2/k+1)-approximation to the maximization (or satisfaction) version of CC rule, and a (1 - 2s/k+1)-approximation to the s-Borda score. This significantly improves the existing submodularity-based analysis of the greedy algorithm that only shows a (1-1/e)-approximation. Our result also improves on the best known approximation algorithm for this problem. We achieve this result by showing that the average dissatisfaction score for the greedy algorithm is at most 2 m+1/k+1 for the CC rule, and at most 2s2 m+1/k+1 for s-Borda. We show these dissatisfaction score bounds are tight up to constants, and even the constant factor of 2 in the case of the CC rule is almost tight. For the dissatisfaction (or minimization) version of the problem, it is known that the average dissatisfaction score of the best committee cannot be approximated in polynomial time to within any constant factor when s is a constant (under standard computational complexity assumptions). As our next result, we strengthen this to show that the score of m+1/k+1 can be viewed as an optimal benchmark for the CC rule, in the sense that it is essentially the best achievable score of any polynomial-time algorithm even when the optimal score is a polynomial factor smaller. We show that another well-studied algorithm for this problem, called the Banzhaf rule, attains this benchmark. We finally show that for the s-Borda rule, when the optimal value is small, these algorithms can be improved by a factor of ~Ømega(√s) via LP rounding. Our upper and lower bounds are a significant improvement over previous results, and taken together, not only enable us to perform a finer comparison of greedy algorithms for these problems, but also provide analytic justification for using such algorithms in practice.

Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well known PageRank interpret a directed edge as a vote in favor of the importance of the linked node. We study the case where nodes may belong to diverse communities or interests and investigate centrality measures that can identify nodes that are simultaneously important to many such diverse communities. We propose a family of diverse centrality measures formed as fixed point solutions to a generalized nonlinear eigenvalue problem. Our measure can be efficiently computed on large graphs by iterated best response and we study its normative properties on both random graph models and real-world data. We find that we are consistently and efficiently able to identify the most important diverse nodes of a graph, that is, those that are simultaneously central to multiple communities.

We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian social cost (OPT). The k'th moment of Distortion is the expected approximation factor with respect to the k'th power of OPT. We consider mechanisms that elicit alternatives by randomly sampling voters for their favorite alternative. We design two families of mechanisms that provide constant (with respect to the number of voters and alternatives) k'th moment of Distortion using just k samples if all voters can then participate in a vote among the proposed alternatives, or 2k-1 samples if only the sampled voters can participate. We also show that these numbers of samples are tight. Such mechanisms deviate from a constant approximation to OPT with probability that drops exponentially in the number of samples, independent of the total number of voters and alternatives. We conclude with simulations on real-world Participatory Budgeting data to qualitatively complement our theoretical insights.

Inspired by traffic routing applications, we consider the problem of finding the shortest path from a source $s$ to a destination $t$ in a graph, when the lengths of the edges are unknown. Instead, we are given {\em hints} or predictions of the edge lengths from a collection of ML models, trained possibly on historical data and other contexts in the network. Additionally, we assume that the true length of any candidate path can be obtained by {\em probing} an up-to-date snapshot of the network. However, each probe introduces a latency, and thus the goal is to minimize the number of probes while finding a near-optimal path with high probability. We formalize this problem and show assumptions under which it admits to efficient approximation algorithms. We verify these assumptions and validate the performance of our algorithms on real data.

In the committee selection problem, we are given m candidates, and n voters. Candidates can have different weights. A committee is a subset of candidates, and its weight is the sum of weights of its candidates. Each voter expresses an ordinal ranking over all possible committees. The only assumption we make on preferences is monotonicity: If S ⊆ S′ are two committees, then any voter weakly prefers S′ to S.

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize Distortion, the worst case social cost of an ordinal mechanism relative to underlying cardinal utilities. We consider two additional desiderata: Constant sample complexity and Squared Distortion. Constant sample complexity means that the mechanism (potentially randomized) only uses a constant number of ordinal queries regardless of the number of voters and alternatives. Squared Distortion is a measure of variance of the Distortion of a randomized mechanism.Our primary contribution is the first social choice mechanism with constant sample complexity and constant Squared Distortion (which also implies constant Distortion). We call the mechanism Random Referee, because it uses a random agent to compare two alternatives that are the favorites of two other random agents. We prove that the use of a comparison query is necessary: no mechanism that only elicits the top-k preferred alternatives of voters (for constant k) can have Squared Distortion that is sublinear in the number of alternatives. We also prove that unlike any top-k only mechanism, the Distortion of Random Referee meaningfully improves on benign metric spaces, using the Euclidean plane as a canonical example. Finally, among top-1 only mechanisms, we introduce Random Oligarchy. The mechanism asks just 3 queries and is essentially optimal among the class of such mechanisms with respect to Distortion.In summary, we demonstrate the surprising power of constant sample complexity mechanisms generally, and just three random voters in particular, to provide some of the best known results in the implicit utilitarian framework.

We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering n points with k centers, we define fairness as proportionality to mean that any n/k points are entitled to form their own cluster if there is another center that is closer in distance for all n/k points. We seek clustering solutions to which there are no such justified complaints from any subsets of agents, without assuming any a priori notion of protected subsets. We present and analyze algorithms to efficiently compute, optimize, and audit proportional solutions. We conclude with an empirical examination of the tradeoff between proportional solutions and the k-means objective.

Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a algorithm called Iterative Local Voting for collective decision-making in this setting. In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm, with the size of the ball shrinking at a specified rate. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to Pareto optimal solutions with desirable fairness properties in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution.We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 2,000 workers, employing neighborhoods defined by various L-Norm balls. We make several observations that inform future implementations of such a procedure.

We propose a model for subtrajectory clustering ---the clustering of subsequences of trajectories; each cluster of subtrajectories is represented as a pathlet, a sequence of points that is not necessarily a subsequence of an input trajectory. Given a set of trajectories, our clustering model attempts to capture the shared portions between them by assuming each trajectory is a concatenation of a small set of pathlets, with possible gaps in between. We present a single objective function for finding the optimal collection of pathlets that best represents the trajectories taking into account noise and other artifacts of the data. We show that the subtrajectory clustering problem is NP-Hard and present fast approximation algorithms for subtrajectory clustering. We further improve the running time of our algorithm if the input trajectories are "well-behaved." Finally, we present experimental results on both real and synthetic data sets. We show via visualization and quantitative analysis that the algorithm indeed handles the desiderata of being robust to variations, being efficient and accurate, and being data-driven.

We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across elements. Our model generalizes existing frameworks such as fair public decision making and participatory budgeting. We study a groupwise fairness notion called the core, which generalizes well-studied notions of proportionality and Pareto efficiency, and requires that each subset of agents must receive an outcome that is fair relative to its size. In contrast to the case of divisible public goods (where fractional allocations are permitted), the core is not guaranteed to exist when allocating indivisible public goods. Our primary contributions are the notion of an additive approximation to the core (with a tiny multiplicative loss), and polynomial time algorithms that achieve a small additive approximation, where the additive factor is relative to the largest utility of an agent for an element. If the feasibility constraints define a matroid, we show an additive approximation of 2. A similar approach yields a constant additive bound when the feasibility constraints define a matching. For feasibility constraints defining an arbitrary packing polytope with mild restrictions, we show an additive guarantee that is logarithmic in the width of the polytope. Our algorithms are based on the convex program for maximizing the Nash social welfare, but differ significantly from previous work in how it is used. As far as we are aware, our work is the first to approximate the core in indivisible settings.

We introduce and study a general scheduling problem that we term the Polytope Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes, and the rates assigned by the scheduler to the jobs are subject to arbitrary packing constraints. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. We show a surprising result—there is a single algorithm that is O (1) competitive for all PSP instances when the objective is total completion time, and O (1) competitive for a large sub-class of PSP instances when the objective is total flow time. This algorithm simply uses the well-known Proportional Fairness (PF) algorithm to perform allocations each time instant. Though P F has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and general settings for optimizing job latency. Further, P F is non-clairvoyant, meaning that the algorithm doesn’t need to know jobs sizes until their completion. We establish our positive results by making novel connections with Economics, in particular, the notions of market clearing, Gross Substitutes, and Eisenberg-Gale markets. We complement these positive results with a negative result: We show that for the total flow time objective, any non-clairvoyant algorithm for general PSP has a strong lower bound on the competitive ratio unless given a poly-logarithmic speed augmentation. This motivates the need to consider sub-classes of PSP when studying flow time. The sub-class for which we obtain positive results not only captures several well-studied models, such as scheduling with speedup curves and related machine scheduling, but also captures as special cases hitherto unstudied scheduling problems, such as single source flow routing, routing multicast (video-on-demand) trees, and resource allocation with substitute resources.

We study social choice rules under the utilitarian distortion framework, with an additional metric assumption on the agents' costs over the alternatives. In this approach, these costs are given by an underlying metric on the set of all agents plus alternatives. Social choice rules have access to only the ordinal preferences of agents but not the latent cardinal costs that induce them. Distortion is then defined as the ratio between the social cost (typically the sum of agent costs) of the alternative chosen by the mechanism at hand, and that of the optimal alternative chosen by an omniscient algorithm. The worst-case distortion of a social choice rule is, therefore, a measure of how close it always gets to the optimal alternative without any knowledge of the underlying costs. Under this model, it has been conjectured that Ranked Pairs, the well-known weighted-tournament rule, achieves a distortion of at most 3 (Anshelevich et al. 2015). We disprove this conjecture by constructing a sequence of instances which shows that the worst-case distortion of Ranked Pairs is at least 5. Our lower bound on the worst-case distortion of Ranked Pairs matches a previously known upper bound for the Copeland rule, proving that in the worst case, the simpler Copeland rule is at least as good as Ranked Pairs. And as long as we are limited to (weighted or unweighted) tournament rules, we demonstrate that randomization cannot help achieve an expected worst-case distortion of less than 3. Using the concept of approximate majorization within the distortion framework, we prove that Copeland and Randomized Dictatorship achieve low constant factor fairness-ratios (5 and 3 respectively), which is a considerable generalization of similar results for the sum of costs and single largest cost objectives. In addition to all of the above, we outline several interesting directions for further research in this space.

Systems for processing big data---e.g., Hadoop, Spark, and massively parallel databases---need to run workloads on behalf of multiple tenants simultaneously. The abundant disk-based storage in these systems is usually complemented by a smaller, but much faster, cache. Cache is a precious resource: Tenants who get to use the cache can see two orders of magnitude performance improvement. Cache is also a limited and hence shared resource: Unlike a resource like a CPU core which can be used by only one tenant at a time, a cached data item can be accessed by multiple tenants at the same time. Cache, therefore, has to be shared by a multi-tenancy-aware policy across tenants, each having a unique set of priorities and workload characteristics.

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. A common feature of many of these two-sided marketplaces is that the platform has full control over search and discovery, but prices are determined by the buyers and sellers. Motivated by this, we study the algorithmic aspects of market segmentation via directed discovery in two-sided markets with endogenous prices. We consider a model where an online platform knows each buyer/seller's characteristics, and associated demand/supply elasticities. Moreover, the platform can use discovery mechanisms (search, recommendation, etc.) to control which buyers/sellers are visible to each other. We develop efficient algorithms for throughput (i.e. volume of trade) and welfare maximization with provable guarantees under a variety of assumptions on the demand and supply functions. We also test the validity of our assumptions on demand curves inferred from NYC taxicab log-data, as well as show the performance of our algorithms on synthetic experiments.

Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a meta-algorithm called Iterative Local Voting for collective decision-making in this setting, in which voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm. In general, such schemes do not converge, or, when they do, the resulting solution does not have a natural description.

Modern data centers consist of a large number of heterogeneous resources such as CPU, memory, network bandwidth, etc. The resources are pooled into clusters for various reasons such as scalability, resource consolidation, and privacy. Clusters are often heterogeneous so that they can better serve jobs with different characteristics submitted from clients. Each job benefits differently depending on how much resource is allocated to the job, which in turn translates to how quickly the job gets completed. In this paper, we formulate this setting, which we term Multi-Cluster Polytope Scheduling (MCPS). In MCPS, a set of n jobs arrive over time to be executed on m clusters. Each cluster i is associated with a polytope P_i, which constrains how fast one can process jobs assigned to the cluster. For MCPS, we seek to optimize the popular objective of minimizing average weighted flow time of jobs in the online setting. We give a constant competitive algorithm with small constant resource augmentation for a large class of polytopes, which capture many interesting problems that arise in practice. Further, our algorithm is non-clairvoyant. Our algorithm and analysis combine and generalize techniques developed in the recent results for the classical unrelated machines scheduling and the polytope scheduling problem [10,12,11].

We propose parallel algorithms in the massively parallel communication (MPC) model (e.g. MapReduce) for processing large terrain elevation data (represented as a 3D point cloud) that are too big to fit on one machine. In particular, given a set S of 3D points that is distributed across multiple machines, we present a simple randomized algorithm to construct a TIN DEM of S by computing the Delaunay triangulation of the xy-projections of points in S, which is also stored across multiple machines. With high probability, the algorithm works in O(1) rounds and the total work performed is O(n log n). Next, we describe an efficient algorithm in the MPC model for computing the contour tree of the resulting DEM. Under some assumptions on the input, the algorithm works in O(1) rounds and the total work performed is O(n log n).

We consider the classical problem of constrained queueing (or switched networks): There is a set of N queues to which unit sized packets arrive. The queues are interdependent, so that at any time step, only a subset of the queues can be activated. One packet from each activated queue can be transmitted, and leaves the system. The set of feasible subsets that can be activated, denoted S, is downward closed and is known in advance. The goal is to find a scheduling policy that minimizes average delay (or flow time) of the packets. The constrained queueing problem models several practical settings including packet transmission in wireless networks and scheduling cross-bar switches. In this paper, we study this problem using the the competitive analysis: The packet arrivals can be adversarial and the scheduling policy only uses information about packets currently queued in the system. We present an online algorithm, that for any epsilon > 0, has average flow time at most O(R^2/epsilon^3*OPT+NR) when given (1+epsilon) speed, i.e., the ability to schedule (1+epsilon) packets on average per time step. Here, R is the maximum number of queues that can be simultaneously scheduled, and OPT is the average flow time of the optimal policy. This asymptotic competitive ratio O(R^3/epsilon^3) improves upon the previous O(N/epsilon^2) which was obtained in the context of multi-dimensional scheduling [Im/Kulkarni/Munagala, FOCS 2015]. In the full general model where N can be exponentially larger than R, this is an exponential improvement. The algorithm presented in this paper is based on Makespan estimates which is very different from that in [Im/Kulkarni/Munagala, FOCS 2015], a variation of the Max-Weight algorithm. Further, our policy is myopic, meaning that scheduling decisions at any step are based only on the current composition of the queues. We finally show that speed augmentation is necessary to achieve any bounded competitive ratio.

With the massive amounts of data available today, it is common to store and process data using multiple machines. Parallel programming platforms such as MapReduce and its variants are popular frameworks for handling such large data. We present the first provably efficient algorithms to compute, store, and query data structures for range queries and approximate nearest neighbor queries in a popular parallel computing abstraction that captures the salient features of MapReduce and other massively parallel communication (MPC) models. In particular, we describe algorithms for $kd$-trees, range trees, and BBD-trees that only require O(1) rounds of communication for both preprocessing and querying while staying competitive in terms of running time and workload to their classical counterparts. Our algorithms are randomized, but they can be made deterministic at some increase in their running time and workload while keeping the number of rounds of communication to be constant.

Many scheduling problems can be viewed as allocating rates to jobs, subject to convex packing constraints on the rates. In this paper, we consider the problem of rate allocation when jobs of unknown size arrive online (non-clairvoyant setting), with the goal of minimizing weighted delay or flow time. Though this problem has strong lower bounds on competitive ratio in its full generality, we show positive results for natural and fairly broad sub-classes. More specifically, the subclasses we consider not only generalize several well-studied models such as scheduling with speedup curves and related machine scheduling, but also capture as special cases hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We establish several first positive results by making connections with two disparate disciplines: Economics and Queueing theory. First, we view the instantaneous allocation of rates as a resource allocation problem. We analyze the natural proportional fairness algorithm from economics. To do this, we extend results from market clearing literature, particularly the Eisenberg-Gale markets and the notions of Walrasian equilibria and Gross Substitutes. This yields the first constant competitive algorithm with constant speed augmentation for single-sink flow routing, routing multicast trees, and multidimensional resource allocation with substitutes resources. Next, we consider the general scheduling problem with packing constraints on rates, but with the restriction that the number of different job types is fixed. We model this problem as a non-stochastic queueing problem. We generalize a natural algorithm from queueing literature and analyze it by extending queueing theoretic ideas. We show that the competitive ratio, for any constant speed, depends polynomially only on the number of job types. Further, such a dependence on the number of job types is unavoidable for non-clairvoyant algorithms. This yields the first algorithm for scheduling multicommodity flows whose competitive ratio depends polynomially on the size of the underlying graph, and not on the number of jobs.

Unwanted friend requests in online social networks (OSNs), also known as friend spam, are among the most evasive malicious activities. Friend spam can result in OSN links that do not correspond to social relationship among users, thus pollute the underlying social graph upon which core OSN functionalities are built, including social search engine, ad targeting, and OSN defense systems. To effectively detect the fake accounts that act as friend spammers, we propose a system called Rejecto. It stems from the observation on social rejections in OSNs, i.e., Even well-maintained fake accounts inevitably have their friend requests rejected or they are reported by legitimate users. Our key insight is to partition the social graph into two regions such that the aggregate acceptance rate of friend requests from one region to the other is minimized. This design leads to reliable detection of a region that comprises friend spammers, regardless of the request collusion among the spammers. Meanwhile, it is resilient to other strategic manipulations. To efficiently obtain the graph cut, we extend the Kernighan-Lin heuristic and use it to iteratively detect the fake accounts that send out friend spam. Our evaluation shows that Rejecto can discern friend spammers under a broad range of scenarios and that it is computationally practical.

The Thompson Sampling (TS) policy is a widely implemented algorithm for the stochastic multi-armed bandit (MAB) problem. Given a prior distribution over possible parameter settings of the underlying reward distributions of the arms, at each time instant, the policy plays an arm with probability equal to the probability that this arm has largest mean reward conditioned on the current posterior distributions of the arms. This policy generalizes the celebrated “probability matching” heuristic which has been experimentally and widely observed in human decision making. However, despite its ubiquity, the Thompson Sampling policy is poorly understood. Our goal in this paper is to make progress towards understanding the empirical success of this policy. We proceed using the lens of approximation algorithms and problem definitions from stochastic optimization. We focus on an objective function termed \em stochastic regret that captures the expected number of times the policy plays an arm that is not the eventual best arm, where the expectation is over the prior distribution. Given such a definition, we show that TS is a 2–approximation to the optimal decision policy in two extreme but canonical scenarios. One such scenario is the two-armed bandit problem which is used as a calibration point in all bandit literature. The second scenario is stochastic optimization where the outcome of a random variable is revealed in a single play to a high or low deterministic value. We show that the 2 approximation is tight in both these scenarios. We provide an uniform analysis framework that in theory is capable of proving our conjecture that the TS policy is a 2–approximation to the optimal decision policy for minimizing stochastic regret, for any prior distribution and any time horizon.

We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online non-clairvoyant setting. In this problem, a set of jobs J arrive over time to be scheduled on a set of M machines. Each job J has processing length pj, weight wj, and is processed at a rate of lij when scheduled on machine i. The online scheduler knows the values of wj and lij upon arrival of the job, but is not aware of the quantity pj. We present the first online algorithm that is scalable ((1+ε)-speed O(1/2)-competitive for any constant ε > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations. We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines. In this problem, each machine can be sped up by a factor of f-1i(P) when consuming power P, where fi is an arbitrary strictly convex power function. In particular, we get an O(γ2)-competitive algorithm when all power functions are of form sγ. These are the first non-trivial non-clairvoyant results in any setting with heterogeneous machines. The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms.

We study the price of anarchy of coordination mechanisms for a scheduling problem where each job j has a weight wj, processing time pij, assignment cost hij, and communication delay (or release date) rij, on machine i. Each machine is free to declare its own scheduling policy. Each job is a selfish agent and selects a machine that minimizes its own disutility, which is equal to its weighted completion time plus its assignment cost. The goal is to minimize the total disutility incurred by all the jobs. Our model is general enough to capture scheduling jobs in a distributed environment with heterogeneous machines (or data centers) that are situated across different locations.

We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling.

Our opinions and judgments are increasingly shaped by what we read on social media -- whether they be tweets and posts in social networks, blog posts, or review boards. These opinions could be about topics such as consumer products, politics, life style, or celebrities. Understanding how users in a network update opinions based on their neighbor's opinions, as well as what global opinion structure is implied when users iteratively update opinions, is important in the context of viral marketing and information dissemination, as well as targeting messages to users in the network.

We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to pseudo-polynomial in parameters that depend on single agent instead of depending on the size of the joint type space. We use this framework to design computationally efficient optimal auctions that satisfy ex-post Individual Rationality in the presence of constraints such as (hard, private) budgets and envy-freeness. We also design optimal auctions when buyers and a seller's utility functions are non-linear. Scenarios with such functions include (a) auctions with "quitting rights", (b) cost to borrow money beyond budget, (c) a seller's and buyers' risk aversion. Finally, we show how our framework also yields optimal auctions for variety of auction settings considered in Alaei et al and Cai et al, albeit with pseudo-polynomial running times.

We present game-theoretic models of opinion formation in social networks where opinions themselves co-evolve with friendships. In these models, nodes form their opinions by maximizing agreements with friends weighted by the strength of the relationships, which in turn depend on difference in opinion with the respective friends. We define a social cost of this process by generalizing recent work of Bindel et al., FOCS 2011. We tightly bound the price of anarchy of the resulting dynamics via local smoothness arguments, and characterize it as a function of how much nodes value their own (intrinsic) opinion, as well as how strongly they weigh links to friends with whom they agree more.

With the advent of social networks such as Facebook and LinkedIn, and online offers/deals web sites, network externalties raise the possibility of marketing and advertising to users based on influence they derive from their neighbors in such networks. Indeed, a user's knowledge of which of his neighbors "liked" the product, changes his valuation for the product. Much of the work on the mechanism design under network externalities has addressed the setting when there is only one product. We consider a more natural setting when there are multiple competing products, and each node in the network is a unit-demand agent.

In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance, itself becomes an interesting and important optimization problem. This general problem is the focus of this article. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas nonadaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor approximations to the optimal observation schemes for several widely used scheduling and metric objective functions. We show a unifying technique that relates this optimization problem to the outlier version of the corresponding deterministic optimization. By making this connection, our technique shows constant factor upper bounds for the benefit of adaptivity of the observation schemes. We show that while probing yields significant improvement in the objective function, being adaptive about the probing is not beneficial beyond constant factors.

Modern wireless interfaces support a physical-layer capability called Message in Message (MIM). Briefly, MIM allows a receiver to disengage from an ongoing reception and engage onto a stronger incoming signal. Links that otherwise conflict with each other can be made concurrent with MIM. However, the concurrency is not immediate and can be achieved only if conflicting links begin transmission in a specific order. The importance of link order is new in wireless research, motivating MIM-aware revisions to link-scheduling protocols. This paper identifies the opportunity in MIM-aware reordering, characterizes the optimal improvement in throughput, and designs a link-layer protocol for enterprise wireless LANs to achieve it. Testbed and simulation results confirm the performance gains of the proposed system.

We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder's value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder's value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these settings, we provide a e/e+1-approximation. We also give a $0.25$-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

In commerce search, the set of products returned by a search engine often forms the basis for all user interactions leading up to a potential transaction on the web. Such a set of products is known as the consideration set. In this study, we consider the problem of generating consideration set of products in commerce search so as to maximize user satisfaction. One of the key features of commerce search that we exploit in our study is the association of a set of important attributes with the products and a set of specified attributes with the user queries. Those important attributes not used in the query are treated as unspecified. The attribute space admits a natural definition of user satisfaction via user preferences on the attributes and their values, viz. require that the surfaced products be close to the specified attribute values in the query, and diverse with respect to the unspecified attributes. We model this as a general Max-Sum Dispersion problem wherein we are given a set of n nodes in a metric space and the objective is to select a subset of nodes with total cost at most a given budget, and maximize the sum of the pairwise distances between the selected nodes. In our setting, each node denotes a product, the cost of a node being inversely proportional to its relevance with respect to specified attributes. The distance between two nodes quantifies the diversity with respect to the unspecified attributes. The problem is NP-hard and a 2-approximation was previously known only when all the nodes have unit cost.

In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentive-compatible auction achieving Pareto-optimality. They further show that this auction is not truthful with private budgets, so that there is no deterministic Pareto-optimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that the adaptive clinching auction is incentive compatible when over-reporting the budget is not possible (for instance, when funds must be shown upfront). We can also make reporting larger budgets suboptimal with a small randomized modification to the auction. In either case, this makes the modified auction Pareto-optimal with private budgets. We also show that the Budget Monotonicity property does not hold for auctioning indivisible units of the good, showing a sharp contrast between the divisible and indivisible cases. The Budget Monotonicity property also implies other improved results in this context. For revenue maximization, the same auction improves the best-known competitive ratio due to Abrams [1] by a factor of 4, and asymptotically approaches the performance of the optimal single-price auction. Finally, we consider the problem of revenue maximization (or social welfare) in a Bayesian setting. We allow the bidders have public size constraints (on the amount of good they are willing to buy) in addition to private budget constraints. We show a simple poly-time computable 5.83-approximation to the optimal Bayesian incentive compatible mechanism, that is implementable in dominant strategies. Our technique again crucially needs the ability to prevent bidders from over-reporting budgets via randomization. We show the approximation result via designing a rounding scheme for an LP relaxation of the problem, which may be of independent interest.

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders have arbitrary demand and budget constraints (and additive valuations). Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with a discrete type space for each bidder, where her valuations for different items can be correlated. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles.

The restless bandit problem is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit (MAB) problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate to any nontrivial factor, and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty. In this article, we consider the Feedback MAB problem, where the reward obtained by playing each of n independent arms varies according to an underlying on/off Markov process whose exact state is only revealed when the arm is played. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is also an instance of a Partially Observable Markov Decision Process (POMDP), and is widely studied in wireless scheduling and unmanned aerial vehicle (UAV) routing. Unlike the stochastic MAB problem, the Feedback MAB problem does not admit to greedy index-based optimal policies. We develop a novel duality-based algorithmic technique that yields a surprisingly simple and intuitive (2+ϵ)-approximate greedy policy to this problem. We show that both in terms of approximation factor and computational efficiency, our policy is closely related to the Whittle index , which is widely used for its simplicity and efficiency of computation. Subsequently we define a multi-state generalization, that we term Monotone bandits, which remains subclass of the restless bandit problem. We show that our policy remains a 2-approximation in this setting, and further, our technique is robust enough to incorporate various side-constraints such as blocking plays, switching costs, and even models where determining the state of an arm is a separate operation from playing it. Our technique is also of independent interest for other restless bandit problems, and we provide an example in nonpreemptive machine replenishment. Interestingly, in this case, our policy provides a constant factor guarantee, whereas the Whittle index is provably polynomially worse. By presenting the first O(1) approximations for nontrivial instances of restless bandits as well as of POMDPs, our work initiates the study of approximation algorithms in both these contexts.

In several systems applications, parameters such as load are known only with some associated uncertainty, which is specified, or modeled, as a distribution over values. The performance of the system optimization and monitoring schemes can be improved by spending resources such as time or bandwidth in observing or resolving the values of these parameters. In a resource-constrained situation, deciding which parameters to observe in order to best optimize the expected system performance (or in general, optimize the expected value of a certain objective function) itself becomes an interesting optimization problem. In this article, we initiate the study of such problems that we term “model-driven optimization”. In particular, we study the problem of optimizing the minimum value in the presence of observable distributions. We show that this problem is NP-Hard, and present greedy algorithms with good performance bounds. The proof of the performance bounds are via novel sub-modularity arguments and connections to covering integer programs.

Failures of Internet services and enterprise systems lead to user dissatisfaction and considerable loss of revenue. Since manual diagnosis is often laborious and slow, there is considerable interest in tools that can diagnose the cause of failures quickly and automatically from system-monitoring data. This paper identifies two key data-mining problems arising in a platform for automated diagnosis called Fa. Fa uses monitoring data to construct a database of failure signatures against which data from undiagnosed failures can be matched. Two novel challenges we address are to make signatures robust to the noisy monitoring data in production systems, and to generate reliable confidence estimates for matches. Fa uses a new technique called anomaly- based clustering when the signature database has no high- confidence match for an undiagnosed failure. This technique clusters monitoring data based on how it differs from the failure data, and pinpoints attributes linked to the failure. We show the effectiveness of Fa through a comprehensive experimental evaluation based on failures from a production setting, a variety of failures injected in a testbed, and synthetic data.

Modern wireless interfaces support a physical layer capability called Message in Message (MIM). Briefly, MIM allows a receiver to disengage from an ongoing reception, and engage onto a stronger incoming signal. Links that otherwise conflict with each other, can be made concurrent with MIM. However, the concurrency is not immediate, and can be achieved only if conflicting links begin transmission in a specific order. The importance of link order is new in wireless research, motivating MIM-aware revisions to link scheduling protocols. This paper identifies the opportunity in MIM-aware reordering, characterizes the optimal improvement in throughput, and designs a link layer protocol to achieve it. Testbed results confirm the performance gains of the proposed system.

Database technology is playing an increasingly important role in understanding and solving large-scale and complex scientific and societal problems and phenomena, for instance, understanding biological networks, climate modeling, electronic markets, etc. In these settings, uncertainty or imprecise information is a pervasive issue that becomes a serious impediment to understanding and effectively utilizing such systems. Clustering is one of the key problems in this context.

The database community has made rapid strides in capturing, representing, and querying uncertain data. Probabilistic databases capture the inherent uncertainty in derived tuples as probability estimates. Data acquisition and stream systems can produce succinct summaries of very large and time-varying datasets. This tutorial addresses the natural next step in harnessing uncertain data: How can we efficiently and quantifiably determine what, how, and how much to learn in order to make good decisions based on the imprecise information available.

In this paper, we consider the restless bandit problem, which is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate to any non-trivial factor, and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty. We make progress on this problem by showing that for an interesting and general subclass that we term Monotone bandits, a surprisingly simple and intuitive greedy policy yields a factor 2 approximation. Such greedy policies are termed index policies, and are popular due to their simplicity and their optimality for the stochastic multi-armed bandit problem. The Monotone bandit problem strictly generalizes the stochastic multi-armed bandit problem, and naturally models multi-project scheduling where the state of a project becomes increasingly uncertain when the project is not scheduled. We develop several novel techniques in the design and analysis of the index policy. Our algorithm proceeds by introducing a novel “balance” constraint to the dual of a well-known LP relaxation to the restless bandit problem. This is followed by a structural characterization of the optimal solution by using both the exact primal as well as dual complementary slackness conditions. This yields an interpretation of the dual variables as potential functions from which we derive the index policy and the associated analysis.

Search auctions have become a dominant source of revenue generation on the Internet. Such auctions have typically used per-click bidding and pricing. We propose the use of hybrid auctions where an advertiser can make a per-impression as well as a per-click bid, and the auctioneer then chooses one of the two as the pricing mechanism. We assume that the advertiser and the auctioneer both have separate beliefs (called priors) on the click-probability of an advertisement. We first prove that the hybrid auction is truthful, assuming that the advertisers are risk-neutral. We then show that this auction is superior to the existing per-click auction in multiple ways: 1. We show that risk-seeking advertisers will choose only a per-impression bid whereas risk-averse advertisers will choose only a per-click bid, and argue that both kind of advertisers arise naturally. Hence, the ability to bid in a hybrid fashion is important to account for the risk characteristics of the advertisers. 2. For obscure keywords, the auctioneer is unlikely to have a very sharp prior on the click-probabilities. In such situations, we show that having the extra information from the advertisers in the form of a per-impression bid can result in significantly higher revenue. 3. An advertiser who believes that its click-probability is much higher than the auctioneer's estimate can use per-impression bids to correct the auctioneer's prior without incurring any extra cost. 4. The hybrid auction can allow the advertiser and auctioneer to implement complex dynamic programming strategies to deal with the uncertainty in the click-probability using the same basic auction. The per-click and per-impression bidding schemes can only be used to implement two extreme cases of these strategies. As Internet commerce matures, we need more sophisticated pricing models to exploit all the information held by each of the participants. We believe that hybrid auctions could be an important step in this direction. The hybrid auction easily extends to multiple slots, and is also applicable to scenarios where the hybrid bidding is per-impression and per-action (i.e. CPM and CPA), or per-click and per-action (i.e. CPC and CPA). Copyright is held by the International World Wide Web Conference Committee (IW3C2).

We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of $O(\log|R|)$, where R is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant load balanced facility location and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor.

The typical workload in a database system consists of a mixture of multiple queries of different types, running concurrently and interacting with each other. Hence, optimizing performance requires reasoning about query mixes and their interactions, rather than considering individual queries or query types. In this paper, we show the significant impact that query interactions can have on workload performance. We present a new approach based on planning experiments and statistical modeling to capture the impact of query interactions. This approach requires no prior assumptions about the internal workings of the database system or the nature or cause of query interactions, making it portable across systems. As a concrete demonstration of the potential of capturing, modeling, and exploiting query interactions, we develop a novel interaction-aware query scheduler that targets report-generation workloads in Business Intelligence (BI) settings. Under certain assumptions, the schedule found by this scheduler is within a constant factor of optimal. An experimental evaluation with TPC-H queries on IBM DB2 demonstrates that our scheduler consistently outperforms (up to 4x) conventional schedulers that do not account for query interactions.

The typical workload in a database system consists of a mixture of multiple queries of different types, running concurrently and interacting with each other. Hence, optimizing performance requires reasoning about query mixes and their interactions, rather than considering individual queries or query types. In this paper, we use such a reasoning approach to develop a query scheduler. We treat the database system as a black box and experimentally build a model to estimate the performance of different query mixes. Our scheduler uses this model to decide which query mixes to schedule, with the goal of maximizing throughput. We experimentally demonstrate the effectiveness of our scheduler using queries from the TPC-H benchmark on DB2.

Many popular Web sites suffer occasional user-visible problems such as slow responses, blank pages or error messages being displayed, items not being added to shopping carts, database slowdowns, and others. Such deviations of systems from desired behavior, or failures, can cause user dissatisfaction and considerable loss of revenue. The scale, complexity, and dynamics of modern systems make it hard to track down the cause of failures manually. We address this problem through a new class of declarative queries, called diagnosis queries, that a system administrator or user can pose to pinpoint the cause of a failure. We describe how diagnosis queries are specified over system-monitoring data, and the challenges faced by current techniques to process these queries. We develop and evaluate a new algorithm, based on a combination of clustering and classification, to process diagnosis queries automatically, efficiently, and with good accuracy.

We present the Cost-Distance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of source-sink distances along an unrelated second metric. We give the first known $O(\log k)$ randomized approximation scheme for Cost-Distance, where k is the number of sources. We reduce several common network design problems to Cost-Distance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include single-sink buy-at-bulk with variable pipe types between different sets of nodes, facility location with buy-at-bulk–type costs on edges (integrated logistics), constructing single-source multicast trees with good cost and delay properties, priority Steiner trees, and multilevel facility location. Our algorithm is also easier to implement and significantly faster than previously known algorithms for buy-at-bulk design problems.

We consider a variant of the classic multi-armed bandit problem (MAB), which we call feedback MAB, where the reward obtained by playing each of n independent arms varies according to an underlying on/off Markov process with known parameters. The evolution of the Markov chain happens irrespective of whether the arm is played, and furthermore, the exact state of the Markov chain is only revealed to the player when the arm is played and the reward observed. At most one arm (or in general, M arms) can be played any time step. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is an instance of a partially observable Markov decision process (POMDP), and a special case of the notoriously intractable "restless bandit" problem. Unlike the stochastic MAB problem, the feedback MAB problem does not admit to greedy index-based optimal policies. Vie state of the system at any time step encodes the beliefs about the states of different arms, and the policy decisions change these beliefs - this aspect complicates the design and analysis of simple algorithms. We design a constant factor approximation to the feedback MAB problem by solving and rounding a natural LP relaxation to this problem. As far as we are aware, this is the first approximation algorithm for a POMDP problem.

We consider the problem of optimizing and executing multiple continuous queries, where each query is a conjunction of filters and each filter may occur in multiple queries. When filters are expensive, significant performance gains are achieved by sharing filter evaluations across queries. A shared execution strategy in our scenario can either be fixed, in which filters are evaluated in the same predetermined order for all input, or adaptive, in which the next filter to be evaluated is chosen at runtime based on the results of the filters evaluated so far. We show that as filter costs increase, the best adaptive strategy is superior to any fixed strategy, despite the overhead of adaptivity. We show that itis NP-hard to find the optimal adaptive strategy, even if we are willing to approximate within any factor smaller than m where m is the number of queries. We then present a greedy adaptive execution strategy and show that it approximates the best adaptive strategy to within a factor O(log2m log n) where n is the number of distinct filters. We also give a precomputation technique that can reduce the execution overhead of adaptive strategies.

We present the first approximation algorithms for a large class of budgeted learning problems. One classicexample of the above is the budgeted multi-armed bandit problem. In this problem each arm of the bandithas an unknown reward distribution on which a prior isspecified as input. The knowledge about the underlying distribution can be refined in the exploration phase by playing the arm and observing the rewards. However, there is a budget on the total number of plays allowed during exploration. After this exploration phase,the arm with the highest (posterior) expected reward is hosen for exploitation. The goal is to design the adaptive exploration phase subject to a budget constraint on the number of plays, in order to maximize the expected reward of the arm chosen for exploitation. While this problem is reasonably well understood in the infinite horizon discounted reward setting, the budgeted version of the problem is NP-Hard. For this problem and several generalizations, we provide approximate policies that achieve a reward within constant factor of the reward optimal policy. Our algorithms use a novel linear program rounding technique based on stochastic packing.

Wireless sensor networks generate a vast amount of data. This data, however, must be sparingly extracted to conserve energy, usually the most precious resource in battery-powered sensors. When approximation is acceptable, a model-driven approach to query processing is effective in saving energy by avoiding contacting nodes whose values can be predicted or are unlikely to be in the result set. To optimize queries such as top-k, however, reasoning directly with models of joint probability distributions can be prohibitively expensive. Instead of using models explicitly, we propose to use samples of past sensor readings. Not only are such samples simple to maintain, but they are also computationally efficient to use in query optimization. With these samples, we can formulate the problem of optimizing approximate top-k queries under an energy constraint as a linear program. We demonstrate the power and flexibility of our sampling-based approach by developing a series of topk query planning algorithms with linear programming, which are capable of efficiently producing plans with better performance and novel features. We show that our approach is both theoretically sound and practically effective on simulated and real-world datasets.

In several database applications, parameters like selectivities and load are known only with some associated uncertainty, which is specified, or modeled, as a distribution over values. The performance of query optimizers and monitoring schemes can be improved by spending resources like time or bandwidth in observing or resolving these parameters, so that better query plans can be generated. In a resource-constrained situation, deciding which parameters to observe in order to best optimize the expected quality of the plan generated (or in general, optimize the expected value of a certain objective function) itself becomes an interesting optimization problem.We present a framework for studying such problems, and present several scenarios arising in anomaly detection in complex systems, monitoring extreme values in sensor networks, load shedding in data stream systems, and estimating rates in wireless channels and minimum latency routes in networks, which can be modeled in this framework with the appropriate objective functions.Even for several simple objective functions, we show the problems are Np-Hard. We present greedy algorithms with good performance bounds. The proof of the performance bounds are via novel sub-modularity arguments.

Monitoring extreme values (MAX or MIN) is a fundamental problem in wireless sensor networks (and in general, complex dynamic systems). This problem presents very different algorithmic challenges from aggregate and selection queries, in the sense that an individual node cannot by itself determine its inclusion in the query result. We present novel query processing algorithms for this problem, with the goal of minimizing message traffic in the network. These algorithms employ a hierarchy of local constraints, or thresholds, to leverage network topology such that message-passing is localized. We evaluate all algorithms using simulated and real-world data to study various trade-offs.

We address the problem of executing continuous multiway join queries in unpredictable and volatile environments. Our query class captures windowed join queries in data stream systems as well as conventional maintenance of materialized join views. Our adaptive approach handles streams of updates whose rates and data characteristics may change over time, as well as changes in system conditions such as memory availability. In this paper we focus specifically on the problem of adaptive placement and removal of caches to optimize join performance. Our approach automatically considers conventional tree-shaped join plans with materialized subresults at every intermediate node, sub result-free MJoins, and the entire spectrum between them. We provide algorithms for selecting caches, monitoring their cost and benefits in current conditions, allocating memory to caches, and adapting as conditions change. All of our algorithms are implemented in the STREAM prototype data stream management system and a thorough experimental evaluation is included.

In sensor networks, data acquisition frequently takes place at low-capability devices. The acquired data is then transmitted through a hierarchy of nodes having progressively increasing network band-width and computational power. We consider the problem of executing queries over these data streams, posed at the root of the hierarchy. To minimize data transmission, it is desirable to perform "in-network" query processing: do some part of the work at intermediate nodes as the data travels to the root. Most previous work on in-network query processing has focused on aggregation and inexpensive filters. In this paper, we address in-network processing for queries involving possibly expensive conjunctive filters, and joins. We consider the problem of placing operators along the nodes of the hierarchy so that the overall cost of computation and data transmission is minimized. We show that the problem is tractable, give an optimal algorithm, and demonstrate that a simpler greedy operator placement algorithm can fail to find the optimal solution. Finally we define a number of interesting variations of the basic operator placement problem and demonstrate their hardness.

We consider the problem of pipelined filters, where a continuous stream of tuples is processed by a set of commutative filters. Pipelined filters are common in stream applications and capture a large class of multiway stream joins. We focus on the problem of ordering the filters adaptively to minimize processing cost in an environment where stream and filter characteristics vary unpredictably over time. Our core algorithm, A-Greedy (for Adaptive Greedy), has strong theoretical guarantees: If stream and filter characteristics were to stabilize, A-Greedy would converge to an ordering within a small constant factor of optimal. (In experiments A-Greedy usually converges to the optimal ordering.) One very important feature of A-Greedy is that it monitors and responds to selectivities that are correlated across filters (i.e., that are nonindependent), which provides the strong quality guarantee but incurs run-time overhead. We identify a three-way tradeoff among provable convergence to good orderings, run-time overhead, and speed of adaptivity. We develop a suite of variants of A-Greedy that lie at different points on this tradeoff spectrum. We have implemented all our algorithms in the STREAM prototype Data Stream Management System and a thorough performance evaluation is presented.

BACKGROUND: A central challenge in the molecular diagnosis and treatment of cancer is to define a set of molecular features that, taken together, distinguish a given cancer, or type of cancer, from all normal cells and tissues. RESULTS: Discriminative margin clustering is a new technique for analyzing high dimensional quantitative datasets, specially applicable to gene expression data from microarray experiments related to cancer. The goal of the analysis is find highly specialized sub-types of a tumor type which are similar in having a small combination of genes which together provide a unique molecular portrait for distinguishing the sub-type from any normal cell or tissue. Detection of the products of these genes can then, in principle, provide a basis for detection and diagnosis of a cancer, and a therapy directed specifically at the distinguishing constellation of molecular features can, in principle, provide a way to eliminate the cancer cells, while minimizing toxicity to any normal cell. CONCLUSIONS: The new methodology yields highly specialized tumor subtypes which are similar in terms of potential diagnostic markers.

We analyze local search heuristics for the metric k-median and facility location problems. We define the locality gap of a local search procedure for a minimization problem as the maximum ratio of a locally optimum solution (obtained using this procedure) to the global optimum. For k-median, we show that local search with swaps has a locality gap of 5. Furthermore, if we permit up to p facilities to be swapped simultaneously, then the locality gap is 3+2/p. This is the first analysis of a local search for k-median that provides a bounded performance guarantee with only k medians. This also improves the previous known 4 approximation for this problem. For uncapacitated facility location, we show that local search, which permits adding, dropping, and swapping a facility, has a locality gap of 3. This improves the bound of 5 given by M. Korupolu, C. Plaxton, and R. Rajaraman [Analysis of a Local Search Heuristic for Facility Location Problems, Technical Report 98-30, DIMACS, 1998]. We also consider a capacitated facility location problem where each facility has a capacity and we are allowed to open multiple copies of a facility. For this problem we introduce a new local search operation which opens one or more copies of a facility and drops zero or more facilities. We prove that this local search has a locality gap between 3 and 4.

Shadow mapping is a technique for doing real-time shadowing. Recent work has shown that shadow mapping hardware can be used as a second depth test in addition to the z-test. In this paper, we explore the computational power provided by this second depth test by examining the problem of rendering objects described as CSG (Constructive Solid Geometry) expressions. We provide an algorithm that asymptotically improves the number of rendering passes required to display a CSG object by a factor of n by exploiting the two-sided depth test. Interestingly, a matching lower bound can be proved demonstrating that our algorithm is optimal.

We consider the problem of incrementally designing a network to route demand to a single sink on an underlying metric space. We are given cables whose costs per unit length scale in a concave fashion with capacity. Under certain natural restrictions on the costs (called the Access Network Design constraints), we present a simple and efficient randomized algorithm that is competitive to the minimum cost solution when the demand points arrive online. In particular, if the order of arrival is a random permutation, we can prove a O(1) competitive ratio. For the fully adversarial case, the algorithm is O(K) -competitive, where K is the number of different pipe types. Since the value of K is typically small, this improves the previous O(log n log log n)-competitive algorithm which was based on probabilistically approximating the underlying metric by a tree metric. Our algorithm also improves the best known approximation ratio and running time for the offline version of this problem.

In this paper, we analyze local search heuristics for the k-median and facility location problems. We define the {\em locality gap\/} of a local search procedure as the maximum ratio of a locally optimum solution (obtained using this procedure) to the global optimum. For k-median, we show that local search with swaps has a locality gap of exactly 5. When we permit p facilities to be swapped simultaneously then the locality gap of the local search procedure is exactly 3+2/p. This is the first analysis of local search for k-median that provides a bounded performance guarantee with only k medians. This also improves the previous known 4 approximation for this problem. For Uncapacitated facility location, we show that local search, which permits adding, dropping and swapping a facility, has a locality gap of exactly 3. This improves the 5 bound of Korupolu et al. We also consider a capacitated facility location problem where each facilitym has a capacity and we are allowed to open multiple copies of a facility. For this problem we introduce a new operation which opens one or more copies of a facility and drops zero or more facilities. We prove that local search which permits this new operation has a locality gap between 3 and 4.

We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(\log |R|), where R is the set of sources. Our algorithms are combinatorial and can be derandomized easily at the cost of a constant factor loss in the approximation ratio.

Gives constant approximations for a number of layered network design problems. We begin by modeling hierarchical caching, where the caches are placed in layers and each layer satisfies a fixed percentage of the demand (bounded miss rates). We present a constant approximation to the minimum total cost of placing the caches and to the routing demand through the layers. We extend this model to cover more general layered caching scenarios, giving a constant combinatorial approximation to the well-studied multi-level facility location problem. We consider a facility location variant, the load-balanced facility location problem, in which every demand is served by a unique facility and each open facility must serve at least a certain amount of demand. By combining load-balanced facility location with our results on hierarchical caching, we give a constant approximation for the access network design problem.

Presents the cost-distance problem, which consists of finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of source-sink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for the cost-distance problem, where k is the number of sources. We reduce several common network design problems to cost-distance problems, obtaining (in some cases) the first known logarithmic approximation for them. These problems include a single-sink buy-at-bulk problem with variable pipe types between different sets of nodes, facility location with buy-at-bulk-type costs on edges, constructing single-source multicast trees with good cost and delay properties, and multi-level facility location. Our algorithm is also easier to implement and significantly faster than previously known algorithms for buy-at-bulk design problems.