Guy Mor-Lan, Omer Goldman, Matan Eyal, Adi Mayrav Gilady, Sivan Eiger, Idan Szpektor, Avinatan Hassidim, Yossi Matias, Reut Tsarfaty. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Navigating health questions can be daunting in the modern information landscape. Large language models (LLMs) may provide tailored, accessible information, but also risk being inaccurate, biased or misleading. We present insights from 5 mixed-methods studies (total N=261), examining how people interact with LLMs for their own health questions. Qualitative studies revealed the importance of context-seeking in conversational AIs to elicit specific details a person may not volunteer or know to share. Context-seeking by LLMs was valued by participants, even if it meant deferring an answer for several turns. Incorporating these insights, we developed a “Wayfinding AI” to proactively solicit context. In two randomized, blinded studies, participants rated the Wayfinding AI as more helpful, relevant, and tailored to their concerns compared to a baseline AI. These results demonstrate the strong impact of proactive context-seeking on conversational dynamics, and suggest design patterns for conversational AI to help navigate health topics.

Given the ubiquity of negative campaigning in recent political elections, we find it important to study its properties from a theoretical computational perspective. To this end, we present a model where elections can be manipulated by convincing voters to demote specific non-favored candidates, and study its properties in the classic setting of scoring rules. When the goal is constructive (making a preferred candidate win), we prove that finding such a demotion strategy is easy for Plurality and Veto, while generally hard for t-approval and Borda. We also provide a min(t, m - t)-factor approximation for t-approval for every t ∈ {1,..., m - 1} (where m is the number of candidates), and a 3-factor approximation algorithm for Borda. Interestingly enough---following recent trends in political science that show that the effectiveness of negative campaigning depends on the type of candidate and demographic---when assigning varying prices to different possible demotion operations, we are able to provide inapproximability results. When the goal is destructive (making the leading opponent lose), we show that the problem is easy for a broad class of scoring rules and provide an FPTAS for the general case.

Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over states (deterministic outcomes) that is leximin in expectation. Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces a lottery that is approximately-leximin (in expectation) - with the same approximation factor. We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.

Fixed-time strategy is a common approach in signal traffic control, characterized by simple and periodic signal plans that are easy to implement without detection mechanisms. A major step in the design of such plans refers to the grouping of the day hours such that the same plan applies for several consecutive hours. The efficacy of the plan, measured by vehicle delays, relies on the matching of traffic with the fixed plan. Accordingly, the time-of-day breakpoints between plans are selected based on the variability of the traffic within each group. The paper studies the selection of time-of-day breakpoints (TODs) based on real traffic characteristics from two cities. Motivated by the Google Green Light project, this study presents an approach to compute TODs based on aggregated traffic statistics computed from anonymized trajectories from navigation applications. We evaluate an optimal dynamic programming algorithm to compute time-of-day breakpoints at an intersection, based on traffic variability among hours. We analyze typical forms of efficient time-of-day breakpoints and examine the impact of the number of daily plans on the ability to predict traffic behavior. We refer to various metrics to measure the variability of the traffic within sets of hours concerning the amount of traffic and its distribution among various movements. We measure the dissimilarity of the time-of-day breakpoints when computed for the different metrics. We also address the joint computation of TODs in adjacent intersections to improve coordination potential.

Every computing paradigm involving communication requires new security protocols employing cryptography. For example, the Internet gave rise to TLS/SSL, and Mobile Computing gave rise to End-to-End Encryption protocols. In this paper, we address an emerging IoT paradigm involving beacons attached to things and security protocols associated with this new configuration. Specifically, we address the “Beacon Notification Problem,” a critical IoT paradigm aimed at providing secure and efficient real-time notifications from beacons to their owners. Since the beacon notification problem has not yet been formally defined, we begin by inspecting natural requirements based on the operational setting and establishing correctness, security, and privacy definitions through the use of cryptographic games. To resolve the beacon notification problem, we propose a novel cryptographic tool we call XDHIES, which is a considerable extension of available Diffie-Hellman encryption schemes. We then show a new notification protocol built upon XDHIES and we prove that this cryptographic protocol is secure and private and successfully meets all the above problem's requirements.

In this paper, we investigate whether the privacy mechanism of periodically changing the pseudorandom identities of Bluetooth Low Energy (BLE) beacons is sufficient to ensure privacy. We consider a new natural privacy notion for BLE broadcasting beacons which we call ``Timed-sequence- indistinguishability'' of beacons. This new privacy definition is stronger than the well-known indistinguishability, since it considers not just the advertisements' content, but also the advertisements' broadcasting times which are observable in the physical world. We then prove that beacons with periodically changing pseudorandom identities do not achieve timed-sequence- indistinguishability. We do this by presenting a novel privacy attack against BLE beacons, which we call the ``Battery Insertion Attack.'' This new time-based privacy attack can be executed by merely inserting or reinserting the beacon's battery at the adversary's chosen time. We performed this attack against an actually deployed beacon. To mitigate the ``Battery Insertion Attack'' and other attacks associated with periodic signaling, we propose a new countermeasure involving quasi-periodic randomized scheduling of identity changes. We prove that our countermeasure ensures timed-sequence indistinguishability for beacons, thereby enhancing the beacon's privacy. Additionally, we show how to integrate this countermeasure in the attacked system while essentially preserving its feasibility and utility, which is crucial for practical industrial adoption.

Reinforcement Learning from Human Feedback (RLHF) has become the standard approach for aligning Large Language Models (LLMs) with human preferences, allowing LLMs to demonstrate remarkable abilities in various tasks. Existing methods work by emulating the human preference at the single decision (turn) level, limiting their capabilities in settings that require planning or multi-turn interactions to achieve a long-term goal. In this paper, we address this issue by developing novel methods for Reinforcement Learning (RL) from preference feedback between two full multi-turn conversations. In the tabular setting, we present a novel mirror-descent-based policy optimization algorithm for the general multi-turn preference-based RL problem, and prove its convergence to Nash equilibrium. To evaluate performance, we create a new environment, Education Dialogue, where a teacher agent guides a student in learning a random topic, and show that a deep RL variant of our algorithm outperforms RLHF baselines. Finally, we show that in an environment with explicit rewards, our algorithm recovers the same performance as a reward-based RL baseline, despite relying solely on a weaker preference signal.

Paul Roit, Johan Ferret, Lior Shani, Roee Aharoni, Geoffrey Cideron, Robert Dadashi, Matthieu Geist, Sertan Girgin, Leonard Hussenot, Orgad Keller, Nikola Momchev, Sabela Ramos Garea, Piotr Stanczyk, Nino Vieillard, Olivier Bachem, Gal Elidan, Avinatan Hassidim, Olivier Pietquin, Idan Szpektor. Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.

Leximin is a common approach to multi-objective optimization, frequently employed in fair division applications. In leximin optimization, one first aims to maximize the smallest objective value; subject to this, one maximizes the second-smallest objective; and so on. Often, even the single-objective problem of maximizing the smallest value cannot be solved accurately. What can we hope to accomplish for leximin optimization in this situation? Recently, Henzinger et al. (2022) defined a notion of approximate leximin optimality. Their definition, however, considers only an additive approximation. In this work, we first define the notion of approximate leximin optimality, allowing both multiplicative and additive errors. We then show how to compute, in polynomial time, such an approximate leximin solution, using an oracle that finds an approximation to a single-objective problem. The approximation factors of the algorithms are closely related: an (α,ϵ)-approximation for the single-objective problem (where α ∈ (0,1] and ϵ ≥ 0 are the multiplicative and additive factors respectively) translates into an (α2/(1 − α + α2), ϵ/(1 − α + α2))-approximation for the multi-objective leximin problem, regardless of the number of objectives. Finally, we apply our algorithm to obtain an approximate leximin solution for the problem of stochastic allocations of indivisible goods.

Or Honovich, Roee Aharoni, Jonathan Herzig, Hagai Taitelbaum, Doron Kukliansy, Vered Cohen, Thomas Scialom, Idan Szpektor, Avinatan Hassidim, Yossi Matias. Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2022.

In recent years, a growing number of students are being assigned to schools through centralized clearinghouses. The success of such clearinghouses crucially relies on the use of a stable matching mechanism [10,12]. The matching market design literature finds that a designer who wishes to implement a stable allocation has limited scope for further design. First, the rural hospital theorem determines that the same positions are filled in all stable allocations [7,9]. Second, the set of stable allocations has the consensus property: all students prefer the outcome of the student-proposing deferred acceptance mechanism (henceforth) to any other stable allocation [4,8]. Third, empirical and theoretical studies suggest that all students, save for a handful, receive the same assignment in all stable allocations [e.g., 1, 2, 5 , 6, 11]. This last finding implies that schools have limited incentive to collect information and to misreport their preferences [3].

A streaming algorithm is said to be adversarially robust if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an adaptive adversary . We establish a connection between adversarial robustness of streaming algorithms and the notion of differential privacy . This connection allows us to design new adversarially robust streaming algorithms that outperform the current state-of-the-art constructions for many interesting regimes of parameters.

Beacons are small devices which are playing an important role in the Internet of Things (IoT), connecting “things” without IP connection to the Internet via Bluetooth Low Energy (BLE) communication. In this paper we present the first private end-to-end encryption protocol called the Eddystone-Ephemeral-ID (Eddystone-EID) protocol. This protocol enables connectivity from any beacon to its remote owner, while supporting beacon’s privacy and security, and essentially preserving the beacon’s low power consumption. We describe the Eddystone-EID development goals, discuss the design decisions, show the cryptographic solution, and analyse its privacy, security, and performance. Finally, we present three secure IoT applications built on Eddystone-EID, demonstrating its utility as a security and privacy infrastructure in the IoT domain. Further, Eddystone-EID is a prototypical example of security design for an asymmetric system in which on one side there are small power-deficient elements (the beacons) and on the other side there is a powerful computing engine (a cloud). The crux of the design strategy is based on: (1) transferring work from the beacon to the cloud, and then (2) building a trade-off between cloud online work against cloud offline work, in order to enable fast real-time reaction of the cloud. These two principles seem to be generic and can be used for other problems in the IoT domain.

Image classification models can depend on multiple different semantic attributes of the image. An explanation of the decision of the classifier needs to both discover and visualize these properties. Here we present StylEx, a method for doing this, by training a generative model to specifically explain multiple attributes that underlie classifier decisions. A natural source for such attributes is the StyleSpace of StyleGAN, which is known to generate semantically meaningful dimensions in the image. However, because standard GAN training is not dependent on the classifier, it may not represent those attributes which are important for the classifier decision, and the dimensions of StyleSpace may represent irrelevant at-tributes. To overcome this, we propose a training procedure for a StyleGAN, which incorporates the classifier model, in order to learn a classifier-specific StyleSpace. Explanatory attributes are then selected from this space. These can be used to visualize the effect of changing multiple attributes per image, thus providing image-specific explanations. We apply StylEx to multiple domains, including animals, leaves, faces and retinal images. For these, we show how an image can be modified in different ways to change its classifier output. Our results show that the method finds attributes that align well with semantic ones, generate meaningful image-specific explanations, and are human-interpretable as measured in user-studies.1

Robustness against adversarial attacks has recently been at the forefront of algorithmic design for machine learning tasks. In the adversarial streaming model, an adversary gives an algorithm a sequence of adaptively chosen updates $u_1,\ldots,u_n$ as a data stream. The goal of the algorithm is to compute or approximate some predetermined function for every prefix of the adversarial stream, but the adversary may generate future updates based on previous outputs of the algorithm. In particular, the adversary may gradually learn the random bits internally used by an algorithm to manipulate dependencies in the input. This is especially problematic as many important problems in the streaming model require randomized algorithms, as they are known to not admit any deterministic algorithms that use sublinear space. In this paper, we introduce adversarially robust streaming algorithms for central machine learning and algorithmic tasks, such as regression and clustering, as well as their more general counterparts, subspace embedding, low-rank approximation, and coreset construction. For regression and other numerical linear algebra related tasks, we consider the row arrival streaming model. Our results are based on a simple, but powerful, observation that many importance sampling-based algorithms give rise to adversarial robustness which is in contrast to sketching based algorithms, which are very prevalent in the streaming literature but suffer from adversarial attacks. In addition, we show that the well-known merge and reduce paradigm in streaming is adversarially robust. Since the merge and reduce paradigm allows coreset constructions in the streaming setting, we thus obtain robust algorithms for $k$-means, $k$-median, $k$-center, Bregman clustering, projective clustering, principal component analysis (PCA) and non-negative matrix factorization. To the best of our knowledge, these are the first adversarially robust results for these problems yet require no new algorithmic implementations. Finally, we empirically confirm the robustness of our algorithms on various adversarial attacks and demonstrate that by contrast, some common existing algorithms are not robust.

We consider a setting of hierarchical reinforcement learning, in which the reward is a sum of components. For each component, we are given a policy that maximizes it, and our goal is to assemble a policy from the individual policies that maximize the sum of the components. We provide theoretical guarantees for assembling such policies in deterministic MDPs with collectible rewards. Our approach builds on formulating this problem as a traveling salesman problem with a discounted reward. We focus on local solutions, i.e., policies that only use information from the current state; thus, they are easy to implement and do not require substantial computational resources. We propose three local stochastic policies and prove that they guarantee better performance than any deterministic local policy in the worst case; experimental results suggest that they also perform better on average.

A streaming algorithm is said to be adversarially robust if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an adaptive adversary. We establish a connection between adversarial robustness of streaming algorithms and the notion of differential privacy. This connection allows us to design new adversarially robust streaming algorithms that outperform the current state-of-the-art constructions for many interesting regimes of parameters.

We consider the classic problem of $(\epsilon,\delta)$-\texttt{PAC} learning a best arm where the goal is to identify with confidence $1-\delta$ an arm whose mean is an $\epsilon$-approximation to that of the highest mean arm in a multi-armed bandit setting. This problem is one of the most fundamental problems in statistics and learning theory, yet somewhat surprisingly its worst case sample complexity is not well understood. In this paper we propose a new approach for $(\epsilon,\delta)$-\texttt{PAC} learning a best arm. This approach leads to an algorithm whose sample complexity converges to \emph{exactly} the optimal sample complexity of $(\epsilon,\delta)$-learning the mean of $n$ arms separately and we complement this result with a conditional matching lower bound. More specifically: \begin{itemize} \item The algorithm's sample complexity converges to \emph{exactly} $\frac{n}{2\epsilon^2}\log \frac{1}{\delta}$ as $n$ grows and $\delta \geq \frac{1}{n}$; % \item We prove that no elimination algorithm obtains sample complexity arbitrarily lower than $\frac{n}{2\epsilon^2}\log \frac{1}{\delta}$. Elimination algorithms is a broad class of $(\epsilon,\delta)$-\texttt{PAC} best arm learning algorithms that includes many algorithms in the literature. \end{itemize} When $n$ is independent of $\delta$ our approach yields an algorithm whose sample complexity converges to $\frac{2n}{\epsilon^2} \log \frac{1}{\delta}$ as $n$ grows. In comparison with the best known algorithm for this problem our approach improves the sample complexity by a factor of over 1500 and over 6000 when $\delta\geq \frac{1}{n}$.

We study conversational domain exploration (CODEX), where the user’s goal is to enrich her knowledge of a given domain by conversing with an informative bot. Such conversations should be well grounded in high-quality domain knowledge as well as engaging and open-ended. A CODEX bot should be proactive and introduce relevant information even if not directly asked for by the user. The bot should also appropriately pivot the conversation to undiscovered regions of the domain. To address these dialogue characteristics, we introduce a novel approach termed dynamic composition that decouples candidate content generation from the flexible composition of bot responses. This allows the bot to control the source, correctness and quality of the offered content, while achieving flexibility via a dialogue manager that selects the most appropriate contents in a compositional manner. We implemented a CODEX bot based on dynamic composition and integrated it into the Google Assistant . As an example domain, the bot conversed about the NBA basketball league in a seamless experience, such that users were not aware whether they were conversing with the vanilla system or the one augmented with our CODEX bot. Results are positive and offer insights into what makes for a good conversation. To the best of our knowledge, this is the first real user experiment of open-ended dialogues as part of a commercial assistant system.

Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition --- increasing-differences.

We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria that we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.

Optimization of machine learning models is commonly performed through stochastic gradient updates on randomly ordered training examples. This practice means that each fraction of an epoch comprises an independent random sample of the training data that may not preserve informative structure present in the full data. We hypothesize that the training can be more effective with self-similar arrangements that potentially allow each epoch to provide benefits of multiple ones. We study this for “matrix factorization” – the common task of learning metric embeddings of entities such as queries, videos, or words from example pairwise associations. We construct arrangements that preserve the weighted Jaccard similarities of rows and columns and experimentally observe training acceleration of 3%-37% on synthetic and recommendation datasets. Principled arrangements of training examples emerge as a novel and potentially powerful enhancement to SGD that merits further exploration.

Automatic speech recognition (ASR) systems have dramatically improved over the last few years. ASR systems are most often trained from 'typical' speech, which means that underrepresented groups don't experience the same level of improvement. In this paper, we present and evaluate finetuning techniques to improve ASR for users with non-standard speech. We focus on two types of non-standard speech: speech from people with amyotrophic lateral sclerosis (ALS) and accented speech. We train personalized models that achieve 62% and 35% relative WER improvement on these two groups, bringing the absolute WER for ALS speakers, on a test set of message bank phrases, down to 10% for mild dysarthria and 20% for more serious dysarthria. We show that 71% of the improvement comes from only 5 minutes of training data. Finetuning a particular subset of layers (with many fewer parameters) often gives better results than finetuning the entire model. This is the first step towards building state of the art ASR models for dysarthric speech.

Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview. The firm wants to recruit the best candidates while minimizing the number of interviews. We model such scenarios as an assignment problem between items (candidates) and categories (departments): the items arrive one-by-one in an online manner, and upon processing each item the algorithm decides, based on its value and the categories it can be matched with, whether to retain or discard it (this decision is irrevocable). The goal is to retain as few items as possible while guaranteeing that the set of retained items contains an optimal matching. We consider two variants of this problem: (i) in the first variant it is assumed that the $n$ items are drawn independently from an unknown distribution $D$. (ii) In the second variant it is assumed that before the process starts, the algorithm has an access to a training set of $n$ items drawn independently from the same unknown distribution (e.g.\ data of candidates from previous recruitment seasons). We give tight bounds on the minimum possible number of retained items in each of these variants. These results demonstrate that one can retain exponentially less items in the second variant (with the training set). Our algorithms and analysis utilize ideas and techniques from statistical learning theory and from discrete algorithms.

We study the problem of coalitional manipulation---where k manipulators try to manipulate an election on m candidates---for any scoring rule, with focus on the Borda protocol. We do so in both the weighted and unweighted settings. For these problems, recent approximation approaches have tried to minimize k, the number of manipulators needed to make some preferred candidate p win (thus assuming that the number of manipulators is not limited in advance). In contrast, we focus on minimizing the score margin of p which is the difference between the maximum score of a candidate and the score of p. We provide algorithms that approximate the optimum score margin, which are applicable to any scoring rule. For the specific case of the Borda protocol in the unweighted setting, our algorithm provides a superior approximation factor for lower values of k.Our methods are novel and adapt techniques from multiprocessor scheduling by carefully rounding an exponentially-large configuration linear program that is solved by using the ellipsoid method with an efficient separation oracle. We believe that such methods could be beneficial in other social choice settings as well.

The classic Bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win. Its important generalizations consider voters who are weighted and also have different prices. We provide an approximate solution for these problems for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: for constant weights and prices, if there exists a strategy which costs k, we efficiently find a strategy which costs at most k+\widetilde{O}(sqrt(k)). An extension for non-constant weights and prices is also given. Our algorithm is based on a randomized reduction from these Bribery generalizations to weighted coalitional manipulation (WCM). To solve this WCM instance, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding a solution in the truncated search space yields a new algorithm for WCM, which is of independent interest.

The classic bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win.We find an approximate solution for this problem for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: if there is a strategy which requires bribing k voters, we efficiently find a strategy which requires bribing at most k + Õ(√k) voters. Our algorithm is based on a randomized reduction from bribery to coalitional manipulation (UCM). To solve the UCM problem, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding the optimal solution in the truncated search space yields a new algorithm for UCM, which is of independent interest.

In a seminal paper, McAfee (1992) presented a truthful mechanism for double auctions, attaining asymptotically-optimal gain-from-trade without any prior information on the valuations of the traders. McAfee's mechanism handles single-parametric agents, allowing each seller to sell a single unit and each buyer to buy a single unit. This paper presents a double-auction mechanism that handles multi-parametric agents and allows multiple units per trader, as long as the valuation functions of all traders have decreasing marginal returns. The mechanism is prior-free, ex-post individually-rational, dominant-strategy truthful and strongly-budget-balanced. Its gain-from-trade approaches the optimum when the market size is sufficiently large.

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely on a novel SDP relaxation for the steady-state distribution of the system. Crucially, and in contrast to previously proposed relaxations, the feasible solutions of our SDP all correspond to “strongly stable” policies that mix exponentially fast to a steady state.

In many practical uses of reinforcement learning (RL) the set of actions available at a given state is a random variable, with realizations governed by an exogenous stochastic process. Somewhat surprisingly, the foundations for such sequential decision processes have been unaddressed. In this work, we formalize and investigate MDPs with stochastic action sets (SAS-MDPs) to provide these foundations. We show that optimal policies and value functions in this model have a structure that admits a compact representation. From an RL perspective, we show that Q-learning with sampled action sets is sound. In model-based settings, we consider two important special cases: when individual actions are available with independent probabilities, and a sampling-based model for unknown distributions. We develop polynomial-time value and policy iteration methods for both cases, and provide a polynomial-time linear programming solution for the first case.

Motivated by applications such as stock exchanges and spectrum auctions, there is a growing interest in mechanisms for arranging trade in two-sided markets. However, existing mechanisms are either not truthful, do not guarantee an asymptotically-optimal gain-from-trade, rely on a prior on the traders' valuations, or operate in limited settings such as a single type of good. We extend the random-sampling technique used in earlier works to multi-good markets where traders have gross-substitute valuations. We show a prior free, truthful and strongly-budget-balanced mechanism which guarantees near-optimal gain from trade when the market sizes of all goods grow to infinity at a similar rate.

We consider the problem of maximizing a submodular function when given access to its approximate version. Submodular functions are heavily studied in a wide variety of disciplines, since they are used to model many real world phenomena, and are amenable to optimization. However, there are many cases in which the phenomena we observe is only approximately submodular and the approximation guarantees cease to hold. We describe a technique which we call the sampled mean approximation that yields strong guarantees for maximization of submodular functions from approximate surrogates under cardinality and intersection of matroid constraints. In particular, we show tight guarantees for maximization under a cardinality constraint and 1/(1+P) approximation under intersection of P matroids.

We present a joint audio-visual model for isolating a single speech signal from a mixture of sounds such as other speakers and background noise. Solving this task using only audio as input is extremely challenging and does not provide an association of the separated speech signals with speakers in the video. In this paper, we present a deep network-based model that incorporates both visual and auditory signals to solve this task. The visual features are used to "focus" the audio on desired speakers in a scene and to improve the speech separation quality. To train our joint audio-visual model, we introduce AVS peech , a new dataset comprised of thousands of hours of video segments from the Web. We demonstrate the applicability of our method to classic speech separation tasks, as well as real-world scenarios involving heated interviews, noisy bars, and screaming children, only requiring the user to specify the face of the person in the video whose speech they want to isolate. Our method shows clear advantage over state-of-the-art audio-only speech separation in cases of mixed speech. In addition, our model, which is speaker-independent (trained once, applicable to any speaker), produces better results than recent audio-visual speech separation methods that are speaker-dependent (require training a separate model for each speaker of interest).

We consider the problem of maximizing a monotone submodular function under noise. Since the 1970s there has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable approximation guarantees. In many applications, however, we do not have access to the submodular function we aim to optimize, but rather to some erroneous or noisy version of it. This raises the question of whether provable guarantees are obtainable in the presence of error and noise. We provide initial answers by focusing on the problem of maximizing a monotone submodular function under a cardinality constraint when given access to a noisy oracle of the function. We show that there is an algorithm whose approximation ratio is arbitrarily close to the optimal $1-1/e$ when the cardinality is sufficiently large. The algorithm can be applied in a variety of related problems including maximizing approximately submodular functions, and optimization with correlated noise. When the noise is adversarial we show that no non-trivial approximation guarantee can be obtained.

We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria which we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.

In this paper we analyze the robustness of stochastic variants of the greedy algorithm for submodular maximization. Our main result shows that for maximizing a monotone submodular function under a cardinality constraint, iteratively selecting an element whose marginal contribution is approximately maximal in expectation is a sufficient condition to obtain the optimal approximation guarantee with exponentially high probability, assuming the cardinality is sufficiently large. One consequence of our result is that the linear-time STOCHASTIC-GREEDY algorithm recently proposed in (Mirzasoleiman et al.,2015) achieves the optimal running time while maintaining an optimal approximation guarantee. We also show that high probability guarantees cannot be obtained for stochastic greedy algorithms under matroid constraints, and prove an approximation guarantee which holds in expectation. In contrast to the guarantees of the greedy algorithm, we show that the approximation ratio of stochastic local search is arbitrarily bad, with high probability, as well as in expectation.

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), Course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several ``items'' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where a X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities.

Prior to 2014, the admission to Master's and PhD programs in psychology in Israel was a mostly decentralized process. In 2013, in response to concerns about the existing procedure, we proposed to use a mechanism that is both stable and strategy-proof for applicants. The first part of this paper describes how we successfully centralized this market, and the critical role of recent advances in the theory of matching with contracts. In the second part of the paper we show empirically (using clearinghouse data) and theoretically that the regularity in preferences with respect to contractual terms leads to a large core. Our results stand in sharp contrast to findings of previous studies on two-sided matching markets without contracts [2, 10, 11, 13]. During the design of the Israeli Psychology Master's Match (IPMM), we met with the faculty of each of the participating programs and asked about the way they choose between applicants. We discovered that departments' choice functions cannot be summarized by a quota and a rank-ordered list (ROL) for each program. Some departments employ affirmative action through minority quotas. Others aim to equalize the number of advisees each faculty member receives. And finally, some departments are willing to admit a limited number of applicants with different contractual terms (e.g., funding). Since terms can alter preferences between programs, this last feature implies that in order to satisfy the aforementioned desiderata, the applicants' message space must be expressive enough to convey their preferences over program-terms pairs. This market is therefore a special case of the matching-with-contracts model [9].

Often one would like to allocate shared resources in a fair way. A common and well-studied notion of fairness isMax-Min Fairness, where we first maximize the smallest allocation, and subject to that the second smallest, and so on. We consider a networking application where multiple commodities compete over the capacity of a network. In our setting, each commodity has multiple possible paths to route its demand (for example, a network using Multiprotocol Label Switching (MPLS) tunneling). In this setting, the only known way of finding a max-min fair allocation requires an iterative solution of multiple linear programs. Such an approach, although polynomial time, scales badly with the size of the network, the number of demands, and the number of paths, and is hard to implement in a distributed environment. More importantly, a network operator has limited control and understanding of the inner working of the algorithm. In this article we introduce Upward Max-Min Fairness, a novel relaxation of Max-Min Fairness, and present a family of simple dynamics that converge to it. These dynamics can be implemented in a distributed manner. Moreover, we present an efficient combinatorial algorithm for finding an upward max-min fair allocation. This algorithm is a natural extension of the well-known Water Filling Algorithm for a multiple path setting. We test the expected behavior of this new algorithm and show that on realistic networks upward max-min fair allocations are comparable to the max-min fair allocations both in fairness and in network utilization.

A mechanism is said to be strategy-proof if no agent has an incentive to misrepresent her true preferences. This property is considered highly desirable for mechanisms that are used in real-life markets. And indeed, many of the great success stories of market design employ strategy-proof mechanisms, such as the second-price sealed-bid auction (Vickrey 1961), or Deferred Acceptance (DA, Gale and Shapley 1962; Dubins and Freedman 1981; Roth 1982). Specifically, in school-choice settings, the appeal of strategy-proof mechanisms is one of the main reasons many school districts choose the applicant-proposing version of DA over pre-existing mechanisms. At the core of the attractiveness of these mechanisms is the assumption that agents report their preferences truthfully in strategy-proof environments.

We consider a simple model of imprecise comparisons: there exists some δ > 0 such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least δ, then the comparison will be made correctly; when the two elements have values that are within δ, the outcome of the comparison is unpredictable. This model is inspired by both imprecision in human judgment of values and also by bounded but potentially adversarial errors in the outcomes of sporting tournaments. Our model is closely related to a number of models commonly considered in the psychophysics literature where δ corresponds to the Just Noticeable Difference (JND) unit or difference threshold . In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences among n elements of a human subject. The method requires performing all ( n 2 ) comparisons, then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decision-making of the human subject, who acts as an imprecise comparator. We show that in our model the method of paired comparisons has optimal accuracy, minimizing the errors introduced by the imprecise comparisons. However, it is also wasteful because it requires all ( n 2 ). We show that the same optimal guarantees can be achieved using 4 n 3/2 comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, max-finding, and selection. Our results provide strong lower bounds and close-to-optimal solutions for each of these problems.

We consider the classic problem of envy-free division of a heterogeneous good (“cake”) among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this article, we replace the entire-allocation requirement with a weaker partial-proportionality requirement: the piece given to each agent must be worth for it at least a certain positive fraction of the entire cake value. We prove that this version of the problem is solvable in bounded time even when the pieces must be connected. We present simple, bounded-time envy-free cake-cutting algorithms for (1) giving each of n agents a connected piece with a positive value; (2) giving each of three agents a connected piece worth at least 1/3; (3) giving each of four agents a connected piece worth at least 1/7; (4) giving each of four agents a disconnected piece worth at least 1/4; and (5) giving each of n agents a disconnected piece worth at least (1 − ϵ)/ n for any positive ϵ.

Hardware-based packet classification has become an essential component in many networking devices. It often relies on ternary content-addressable memories (TCAMs), which compare the packet header against a set of rules. TCAMs are not well suited to encode range rules. Range rules are often encoded by multiple TCAM entries, and little is known about the smallest number of entries that one needs for a specific range. In this paper, we introduce the In/Out TCAM, a new architecture that combines a regular TCAM together with a modified TCAM. This custom architecture enables independent encoding of each rule in a set of rules. We provide the following theoretical results for the new architecture: 1) We give an upper bound on the worst-case expansion of range rules in one and two dimensions. 2) For extremal ranges, which are 89% of the ranges that occur in practice, we provide an efficient algorithm that computes an optimal encoding. 3) We present a closed-form formula for the average expansion of an extremal range.

We present a credit-based matching mechanism for dynamic barter markets — and kidney exchange in particular — that is both strategy proof and efficient, that is, it guarantees truthful disclosure of donor-patient pairs from the transplant centers and results in the maximum global matching. Furthermore, the mechanism is individually rational in the sense that, in the long run, it guarantees each transplant center more matches than the center could have achieved alone. The mechanism does not require assumptions about the underlying distribution of compatibility graphs — a nuance that has previously produced conflicting results in other aspects of theoretical kidney exchange. Our results apply not only to matching via 2-cycles: the matchings can also include cycles of any length and altruist-initiated chains, which is important at least in kidney exchanges. The mechanism can also be adjusted to guarantee immediate individual rationality at the expense of economic efficiency, while preserving strategy proofness via the credits. This circumvents a well-known impossibility result in static kidney exchange concerning the existence of an individually rational, strategy-proof, and maximal mechanism. We show empirically that the mechanism results in significant gains on data from a national kidney exchange that includes 59% of all US transplant centers.

We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of crucial importance in many applications, e.g., squares or bounded aspect-ratio rectangles are most useful for building houses as well as advertisements. We thus introduce and study the problem of envy-free two-dimensional division wherein the utility of the agents depends on the geometric shape of the allocated pieces (as well as the location and size). In addition to envy-freeness, we require that the fraction allocated to each agent be at least a certain constant that depends only on the shape of the cake and the number of agents. We focus on the case where the allotted pieces must be square and the cakes are either squares or the unbounded plane. We provide algorithms for the problem for settings with two and three agents.

No abstract available.

The "law of one price" asserts that homogeneous goods must sell for the same price across locations and vendors. While many deviations from this 'law' have been observed in the real world, it remains a useful building block in economic theory, and serves as a benchmark for empirical studies. A crucial underlying assumption used in arguing for the validity of the law is the homogeneity of goods and buyers: buyers do not care which of the goods they buy, or which seller they are buying it from, nor do sellers care about the identity of the buyers. In other words, any two instances of the good are perfect substitutes for the buyers, as are any two buyers from any seller's point of view. This paper makes the formal claim that even in the presence of heterogeneous preferences, an approximate version of the law remains valid, and the approximation improves as the market grows large.

We introduce the notion of local computation mechanism design - designing game theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments.

With the rise of datacenter virtualization, the number of entries in the forwarding tables of datacenter switches is expected to scale from several thousands to several millions. Unfortunately, such forwarding table sizes would not fit on-chip memory using current implementations. In this paper, we investigate the compressibility of forwarding tables. We first introduce a novel forwarding table architecture with separate encoding in each column. It is designed to keep supporting fast random accesses and fixed-width memory words. Then, we show that although finding the optimal encoding is NP-hard, we can suggest an encoding whose memory requirement per row entry is guaranteed to be within a small additive constant of the optimum. Next, we analyze the common case of two-column forwarding tables, and show that such tables can be presented as bipartite graphs. We deduce graph-theoretical bounds on the encoding size. We also introduce an algorithm for optimal conditional encoding of the second column given an encoding of the first one. In addition, we explain how our architecture can handle table updates. Last, we evaluate our suggested encoding techniques on synthetic forwarding tables as well as on real-life tables.

We introduce a new variant of quantum multiprover interactive proofs (QMIP) where the provers and the verifier are quantum. The verifier can exchange quantum messages with the provers. The provers cannot communicate quantumly between themselves and do not share entanglement, but are unlimited in the classical communication between them, even after receiving messages from the verifier. We show that any language in nondeterministic exponential time (NEXP) can be recognized in this model efficiently, with just two provers and two rounds of communication, and with a constant completeness/soundness gap. This is in contrast to the result of [R. Jain et al., Comm. ACM, 53 (2010), pp. 102--109], which shows that QIP = PSPACE, or equivalently that the set of languages that can be recognized by a quantum verifier communicating with a single quantum prover is equal to PSPACE. To analyze the cheating power of the provers, we give them more power and allow them to perform any separable operation. We then show a unique two-phase protocol in which the provers first commit to a superposition of correct answers to all possible questions, and then in the second phase the verifier opens up the committed answer and checks for correctness and consistency.

Building and operating a large backbone network can take months or even years, and it requires a substantial investment. Therefore, there is an economical drive to increase the utilization of network resources (links, switches, etc.) in order to improve the cost efficiency of the network. At the same time, the utilization of network components has a direct impact on the performance of the network and its resilience to failure, and thus operational considerations are a critical aspect of the decision regarding the desired network load and utilization. However, the actual utilization of the network resources is not easy to predict or control. It depends on many parameters like the traffic demand and the routing scheme (or Traffic Engineering if deployed), and it varies over time and space. As a result it is very difficult to actually define real network utilization and to understand the reasons for this utilization. In this paper we introduce a novel way to look at the network utilization. Unlike traditional approaches that consider the average link utilization, we take the flow perspective and consider the network utilization in terms of the growth potential of the flows in the network. After defining this new Flow Utilization, and discussing how it differs from common definitions of network utilization, we study ways to efficiently compute it over large networks. We then show, using real backbone data, that Flow Utilization is very useful in identifying network state and evaluating performance of TE algorithms.

Hardware-based packet classification has become an essential component in many networking devices. It often relies on TCAMs (ternary content-addressable memories), which need to compare the packet header against a set of rules. But efficiently encoding these rules is not an easy task. In particular, the most complicated rules are range rules, which usually require multiple TCAM entries to encode them. However, little is known on the optimal encoding of such non-trivial rules. In this work, we take steps towards finding an optimal encoding scheme for every possible range rule. We first present an optimal encoding for all possible generalized extremal rules. Such rules represent 89% of all non-trivial rules in a typical real-life classification database. We also suggest a new method of simply calculating the optimal expansion of an extremal range, and present a closed-form formula of the average optimal expansion over all extremal ranges. Next, we present new bounds on the worst-case expansion of general classification rules, both in one-dimensional and two-dimensional ranges. Last, we introduce a new TCAM architecture that can leverage these results by providing a guaranteed expansion on the tough rules, while dealing with simpler rules using a regular TCAM. We conclude by verifying our theoretical results in experiments with synthetic and real-life classification databases.

With the rise of datacenter virtualization, the number of entries in forwarding tables is expected to scale from several thousands to several millions. Unfortunately, such forwarding table sizes can hardly be implemented today in on-chip memory. In this paper, we investigate the compressibility of forwarding tables. We first introduce a novel forwarding table architecture with separate encoding in each column. It is designed to keep supporting fast random accesses and fixed-width memory words. Then, we suggest an encoding whose memory requirement per row entry is guaranteed to be within a small additive constant of the optimum. Next, we analyze the common case of two-column forwarding tables, and show that such tables can be presented as bipartite graphs. We deduce graph-theoretical bounds on the encoding size. We also introduce an algorithm for optimal conditional encoding of the second column given an encoding of the first one. In addition, we explain how our architecture can handle table updates. Last, we evaluate our suggested encoding techniques on synthetic forwarding tables as well as on real-life tables.

Traditional recommender systems minimize prediction error with respect to users' choices. Recent studies have shown that recommender systems have a positive effect on the provider's revenue.

We consider the algorithmic challenges behind a novel interface that simplifies consumer research of online reviews by surfacing relevant comparable review bundles: reviews for two or more of the items being researched, all generated in similar enough circumstances to provide for easy comparison. This can be reviews by the same reviewer, or by the same demographic category of reviewer, or reviews focusing on the same aspect of the items. But such an interface will work only if the review ecosystem often has comparable review bundles for common research tasks.

Often one would like to allocate shared resources in a fair way. A common and well studied notion of fairness is Max-Min Fairness, where we first maximize the smallest allocation, and subject to that the second smallest, and so on. We consider a networking application where multiple commodities compete over the capacity of a network. In our setting each commodity has multiple possible paths to route its demand (for example, a network using MPLS tunneling). In this setting, the only known way of finding a max-min fair allocation requires an iterative solution of multiple linear programs. Such an approach, although polynomial time, scales badly with the size of the network, the number of demands, and the number of paths. More importantly, a network operator has limited control and understanding of the inner working of the algorithm. Finally, this approach is inherently centralized and cannot be implemented via a distributed protocol. In this paper we introduce Upward Max-Min Fairness, a novel relaxation of Max-Min Fairness and present a family of simple dynamics that converge to it. These dynamics can be implemented in a distributed manner. Moreover, we present an efficient combinatorial algorithm for finding an upward max-min fair allocation, which is a natural extension of the well known Water Filling Algorithm for a multiple path setting. We test the expected behavior of this new algorithm and show that on realistic networks upward max-min fair allocations are comparable to the max-min fair allocations both in fairness and in network utilization.

Many practically deployed flow algorithms produce the output as a set of values associated with the network links. However, to actually deploy a flow in a network we often need to represent it as a set of paths between the source and destination nodes. In this paper we consider the problem of decomposing a flow into a small number of paths. We show that there is some fixed constant β >; 1 such that it is NP-hard to find a decomposition in which the number of paths is larger than the optimal by a factor of at most β. Furthermore, this holds even if arcs are associated only with three different flow values. We also show that straightforward greedy algorithms for the problem can produce much larger decompositions than the optimal one, on certain well tailored inputs. On the positive side we present a new approximation algorithm that decomposes all but an c-fraction of the flow into at most O(1/ϵ2) times the smallest possible number of paths. We compare the decompositions produced by these algorithms on real production networks and on synthetically generated data. Our results indicate that the dependency of the decomposition size on the fraction of flow covered is exponential. Hence, covering the last few percent of the flow may be costly, so if the application allows, it may be a good idea to decompose most but not all the flow. The experiments also reveal the fact that while for realistic data the greedy approach works very well, our novel algorithm which has a provable worst case guarantee, typically produces only slightly larger decompositions.

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.

We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth n tree using O(n2+logω) queries, where ω is independent of n and depends only on the type of subformulas within the tree. We also prove a classical lower bound of nΩ(log log n) queries, thus showing a (small) super-polynomial speed-up.

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for large random markets the algorithm will find a stable matching with high probability. In our model we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.

No abstract available.

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.

Suppose one has access to oracles generating samples from two unknown probability distributions p and q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the L1-norm? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the L1-distance ∥p-q∥1can be estimated with a constant precision using only O(N1/2) queries in the quantum settings, whereas classical computers need Ω(N1-o(1)) queries. We also describe quantum algorithms for testing uniformity and orthogonality with query complexity O(N1/3). The classical query complexity of these problems is known to be Ω(N1/2).

Suppose one has access to oracles generating samples from two unknown probability distributions $p$ and $q$ on some $N$-element set. How many samples does one need to test whether the two distributions are close or far from each other in the $L_1$-norm? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the $L_1$-distance $\|p-q\|_1$ can be estimated with a constant precision using only $O(N^{1/2})$ queries in the quantum settings, whereas classical computers need $\Omega(N^{1-o(1)})$ queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity $O(N^{1/3})$. The classical query complexity of these problems is known to be $\Omega(N^{1/2})$. A quantum algorithm for testing Uniformity has been recently independently discovered by Chakraborty et al. \cite{CFMW09}.

We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class of bounded-degree graphs. These oracles utilize only local computation to consistently answer queries about a global partition that breaks the graph into small connected components by removing only a small fraction of the edges. We illustrate the power of this technique by using it to extend and simplify a number of previous approximation and testing results for sparse graphs, as well as to provide new results that were unachievable with existing techniques. For instance:1. We give constant-time approximation algorithms for the size of the minimum vertex cover, the minimum dominating set, and the maximum independent set for any class of graphs with an excluded minor.2. We show a simple proof that any minor-closed graph property is testable in constant time in the bounded degree model.3. We prove that it is possible to approximate the distance to almost any hereditary property in any bounded degree hereditary families of graphs. Hereditary properties of interest include bipartiteness, k-colorability, and perfectness.

A sender holds a word x consisting of n blocks xi, each of t bits, and wishes to broadcast a codeword to m receivers, R1,...,Rm. Each receiver Riis interested in one block, and has prior side information consisting of some subset of the other blocks. Let betatbe the minimum number of bits that has to be transmitted when each block is of length t, and let beta be the limit beta=limtrarrinfinbetat/t. Informally, beta is the average communication cost per bit in each block (for long blocks). Finding the coding rate beta, for such an informed broadcast setting, generalizes several coding theoretic parameters related to Informed Source Coding on Demand, Index Coding and Network Coding. In this work we show that usage of large data blocks may strictly improve upon the trivial encoding which treats each bit in the block independently. To this end, we provide general bounds on betat, and prove that for any constant C there is an explicit broadcast setting in which beta = 2 but beta1> C. One of these examples answers a question of . In addition, we provide examples with the following counterintuitive direct-sum phenomena. Consider a union of several mutually independent broadcast settings. The optimal code for the combined setting may yield a significant saving in communication over concatenating optimal encodings for the individual settings. This result also provides new non-linear coding schemes which improve upon the largest known gap between linear and non-linear Network Coding, thus improving the results of. The proofs are based on a relation between this problem and results in the study of Witsenhausen's rate, OR graph products, colorings of Cayley graphs, and the chromatic numbers of Kneser graphs.

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants:1. Each comparison is erroneous with independent probability 1-p. 2. At each stage k comparisons can be performed in parallel and a noisy answer is returned. We present a (classical) algorithm which solves both variants optimally (with respect to p and k), up to an additive term of O(loglog n), and prove matching information-theoretic lower bounds. We use the algorithm to improve the results of Farhi et al., presenting an exact quantum search algorithm in an ordered list of expected complexity less than (log2n)/3.

We introduce another variant of quantum MIP, where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange information seem to be equivalent in power to a simple prover. This in fact is not the case-we show that any language in NEXP can be recognized in this model efficiently, with just two provers and two rounds of communication, with a constant completeness-soundness gap. Similar ideas and techniques may help help with other models of quantum MIP, including the dual question, of non communicating provers with unlimited entanglement.

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any \left[ {\frac{{n - 1}} {2}} \right] cheaters among n players. Previous protocols for these tasks tolerated \left[ {\frac{{n - 1}} {4}} \right] and \left[ {\frac{{n - 1}} {6}} \right] cheaters, respectively. The threshold we achieve is tight -- even in the classical case, "fair" multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in faulttolerant quantum circuits.

We present a fast quantum Byzantine Agreement protocol that can reach agreement in O(1) expected communication rounds against a strong full information, dynamic adversary, tolerating up to the optimal t‹n3 faulty players in the synchronous setting, and up to t‹n4 faulty players for asynchronous systems. This should be contrasted with the known classical synchronous lower bound of Ω(√ nlog n) [3] when t=(n).