This tutorial will provide a template for how a CS program can combine its discrete math and automata theory offerings into a single course. Doing this serves two purposes. First, this allows course-limited programs (e.g., liberal arts colleges) to offer both courses in a single-semester 4-credit experience. This might help with creating space for other required offerings or to overcome staffing challenges. Second, the introduction of math concepts just in time to learn automata theory gives more motivation to computer science students to learn the math and to see how it will connect to their later CS coursework. This approach has been used by a small liberal arts college (Denison University) for the past 8 years to great success. Students start with minimal prerequisites (introductory CS and high school algebra). The course covers a wide range of topics from discrete math such as sets, strings, languages, logic, direct proof, proof by induction, proof by contradiction, combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. Many of these topics are introduced just in time to learn about topics such as finite automata, regular expressions, closure properties, pumping lemma, context-free grammars, Turing machines, and computability. Students are usually excited to learn about Turing machines and the halting problem this early in the curriculum. This tutorial will share the resources used at Denison to teach this course in a single semester (3 days/week, 15 weeks). These will include a freely available online PDF textbook with over 250 worked examples and 550 exercises.

We propose the indistinguishability query for iden-tifying all of a user's near-optimal tuples. This query returns all the tuples that are at most a small fraction away from the optimal of the user's unknown utility function. This is motivated by the idea that users can have a hard time distinguishing very similar tuples and in fact even tuples that are slightly inferior in the identified criteria may have additional characteristics that make them more attractive to the user. In order to perform this query without knowledge of the user's utility function, we use a simple interactive framework that asks the user to perform a modest number of comparisons to narrow down their utility function. We show that the indistinguishability query cannot be approximated solely with real tuples in the database and thus our algorithms with provable bounds must present the user with artificial tuples. We also give heuristic algorithms that show the user only real tuples from the database. Since the user may make errors while performing comparisons, we generalize our algorithms to account for user error as well. Experiments on synthetic and real data sets show that the indistinguishability query can be performed accurately while asking the user to compare a small number of tuples.

We present space-efficient algorithms for performing Pearson’s chi-square goodness-of-fit test in a streaming setting. Since the chi-square test is one of the most well known and commonly used tests in statistics, it is surprising that there has been no prior work on designing streaming algorithms for it. The test is not based on a specific distribution assumption and has one-sample and two-sample variants. Given a stream of data, the one-sample variant tests if the stream is drawn from a fixed distribution. The two-sample variant tests if two data streams are drawn from the same or similar distributions. One major advantage of using statistical tests over other quantities commonly measured by streaming algorithms is that these tests do not require parameter tuning and have results that can be easily interpreted by data analysts. The problem that we solve in this paper is how to compute the chi-square test on streams with minimal parameter configuration and assumptions. We give rigorous proofs showing that it is possible to compute the chi-square statistic with high fidelity and an almost quadratic reduction in memory in the continuous case, but the categorical case only admits heuristic solutions. We validate the performance and accuracy of our algorithms through extensive testing on both real and synthetic data sets.

When faced with a database containing millions of tuples, an end user might be only interested in finding his/her (close to) favorite tuple in the database. Recently, a regret minimization query was proposed to obtain a small subset from the database that fits the user's needs, which are expressed through an unknown utility function. Specifically, it minimizes the "regret'' level of a user, which we quantify as the regret ratio if s/he gets the best tuple in the selected subset but not the best tuple among all tuples in the database. We study how to enhance the regret minimization query with user interactions : when presented with a small number of tuples (which can be artificial tuples or true tuples inside the database), a user is asked to indicate the tuple s/he favors the most among them. In particular, we are also interested in the special case of determining the favorite tuple for a user in the entire database with a small amount of interaction, measured by the number of questions we ask the user. Different from the previous work which displays artificial tuples to users, we achieve a stronger result in this paper by always displaying true tuples in the database. Specifically, we present a generic framework for interactive regret minimization, under which we propose algorithms that ask an asymptotically optimal number of questions in 2-dimensional spaces and algorithms with provable performance guarantees in d-dimensional spaces ($d \geq 2$) where each dimension corresponds to a description of a tuple. Experiments on real and synthetic datasets showed that our algorithms outperform the existing one by locating the favorite tuple and guaranteeing a small regret ratiowith much fewer questions.

Extracting interesting tuples from a large database is an important problem in multi-criteria decision making. Two representative queries were proposed in the literature: top- k queries and skyline queries. A top- k query requires users to specify their utility functions beforehand and then returns k tuples to the users. A skyline query does not require any utility function from users but it puts no control on the number of tuples returned to users. Recently, a k-regret query was proposed and received attention from the community because it does not require any utility function from users and the output size is controllable, and thus it avoids those deficiencies of top- k queries and skyline queries. Specifically, it returns k tuples that minimize a criterion called the maximum regret ratio .

We propose space-efficient algorithms for performing the Kolmogorov-Smirnov test on streaming data. The Kolmogorov-Smirnov test is a non-parametric test for measuring the strength of a hypothesis that some data is drawn from a fixed distribution (one-sample test), or that two sets of data are drawn from the same distribution (two-sample test). Unlike some other tests, Kolmogorov-Smirnov does not assume that the distribution has a known form (e.g., it is normal), and in the two-sample case it need not know anything about the distribution, other than that it is continuous. Motivated by the challenges of big data, we present algorithms for both the one-sample and the two-sample tests for data processed in a stream. We demonstrate the accuracy of our algorithms via extensive experimentation on both real and synthetic datasets. We show that our algorithms are superior to sampling and that they accurately perform the test with several orders of magnitude reduction in data.

Viral marketing is a powerful tool for online advertising and sales because it exploits the influence people have on one another. While this marketing technique has been beneficial for advertisers, it has not been shown how the social network providers such as Facebook and Twitter can benefit from it. In this paper, we initiate the study of sponsored viral marketing where a social network provider that has complete knowledge of its network is hired by several advertisers to provide viral marketing. Each advertiser has its own advertising budget and a fixed amount they are willing to pay for each user that adopts their product or shares their ads. The goal of the social network provider is to gain the most revenue from the advertisers. Since the products or ads from different advertisers may compete with each other in getting users' attention, and advertisers pay differently per share and have different budgets, it is very important that the social network providers start the "seeds" of the viral marketing of each product at the right places in order to gain the most benefit.

In exploring representative databases, a primary issue has been finding accurate models of user preferences. Given this, our work generalizes the method of regret minimization as proposed by Nanongkai et al. to include nonlinear utility functions. Regret minimization is an approach for selecting k representative points from a database such that every user's ideal point in the entire database is similar to one of the k points. This approach combines benefits of the methods top- k and skyline; it controls the size of the output but does not require knowledge of users' preferences. Prior work with k -regret queries assumes users' preferences to be modeled by linear utility functions. In this paper, we derive upper and lower bounds for nonlinear utility functions, as these functions can better fit occurrences such as diminishing marginal returns, propensity for risk, and substitutability of preferences. To model these phenomena, we analyze a broad subset of convex, concave, and constant elasticity of substitution functions. We also run simulations on real and synthetic data to prove the efficacy of our bounds in practice.

The explosive increase in cellular network traffic, users, and applications, as well as the corresponding shifts in user expectations, has created heavy needs and demands on cellular data providers. In this paper we address one such need: mining the logs of cellular voice and data traffic to rapidly detect network performance anomalies and other events of interest. The core challenge in solving this problem is the issue that it is impossible to predict beforehand where in the traffic the event may appear, requiring us to be able to query arbitrary subsets of the network traffic (e.g., longer than usual round-trip times for users in a specific urban area to connect to FunContent.com using a particular model of phone). Since it is infeasible to store all combinations of such data, especially when it is collected in real-time, we need to be able to summarize the traffic data using succinct sketch data structures to answer these queries.

Error estimating codes (EEC) have recently been proposed for measuring the bit error rate (BER) in packets transmitted over wireless links. They however can provide such measurements only when there are no insertion and deletion errors, which could occur in various wireless network environments. In this work, we propose ``idEEC'', the first technique that can do so even in the presence of insertion and deletion errors. We show that idEEC is provable robust under most bit insertion and deletion scenarios, provided insertion/deletion errors occur with much lower probability than bit flipping errors. Our idEEC design can build upon any existing EEC scheme. The basic idea of the idEEC encoding is to divide the packet into a number of segments, each of which is encoded using the underlying EEC scheme. The basic idea of the idEEC decoding is to divide the packet into a few slices in a randomized manner -- each of which may contain several segments -- and then try to identify a slice that has no insertion and deletion errors in it (called a ``clean slice''). Once such a clean slice is found, it is removed from the packet for later processing, and this ``randomized divide and search'' procedure will be iteratively performed on the rest of the packet until no more clean slices can be found. The BER will then be estimated from all the clean slices discovered through all the iterations. A careful analysis of the accuracy guarantees of the idEEC decoding is provided, and the efficacy of idEEC is further validated by simulation experiments.

We study error estimating codes with the goal of establishing better bounds for the theoretical and empirical overhead of such schemes. We explore the idea of using sketch data structures for this problem, and show that the tug-of-war sketch gives an asymptotically optimal solution. The optimality of our algorithms are proved using communication complexity lower bound techniques. We then propose a novel enhancement of the tug-of-war sketch that greatly reduces the communication overhead for realistic error rates. Our theoretical analysis and assertions are supported by extensive experimental evaluation.

In distributed networks, some groups of nodes may have more inter-connections, perhaps due to their larger bandwidth availability or communication requirements. In many scenarios, it may be useful for the nodes to know if they form part of a dense subgraph, e.g., such a dense subgraph could form a high bandwidth backbone for the network. In this work, we address the problem of self-awareness of nodes in a dynamic network with regards to graph density, i.e., we give distributed algorithms for maintaining dense subgraphs (subgraphs that the member nodes are aware of). The only knowledge that the nodes need is that of the dynamic diameter D, i.e., the maximum number of rounds it takes for a message to traverse the dynamic network. For our work, we consider a model where the number of nodes are fixed, but a powerful adversary can add or remove a limited number of edges from the network at each time step. The communication is by broadcast only and follows the CONGEST model in the sense that only messages of O(log n) size are permitted, where n is the number of nodes in the network.

Error estimating coding (EEC) has recently been established as an important tool to estimate bit error rates in the transmission of packets over wireless links, with a number of potential applications in wireless networks. In this paper, we present an in-depth study of error estimating codes through the lens of Fisher information analysis and find that the original EEC estimator fails to exploit the information contained in its code to the fullest extent. Motivated by this discovery, we design a new estimator for the original EEC algorithm, which significantly improves the estimation accuracy, and is empirically very close to the Cramer-Rao bound. Following this path, we generalize the EEC algorithm to a new family of algorithms called gEEC generalized EEC. These algorithms can be tuned to hold 25-35% more information with the same overhead, and hence deliver even better estimation accuracy---close to optimal, as evidenced by the Cramer-Rao bound. Our theoretical analysis and assertions are supported by extensive experimental evaluation.

We study the notion of regret ratio proposed in [19] Nanongkai et al. [VLDB10] to deal with multi-criteria decision making in database systems. The regret minimization query proposed in [19] Nanongkai et al. was shown to have features of both skyline and top-k: it does not need information from the user but still controls the output size. While this approach is suitable for obtaining a reasonably small regret ratio, it is still open whether one can make the regret ratio arbitrarily small. Moreover, it remains open whether reasonable questions can be asked to the users in order to improve efficiency of the process.

The study of skylines and their variants has received considerable attention in recent years. Skylines are essentially sets of most interesting (undominated) tuples in a database. However, since the skyline is often very large, much research effort has been devoted to identifying a smaller subset of (say k) “representative skyline” points. Several different definitions of representative skylines have been considered. Most of these formulations are intuitive in that they try to achieve some kind of clustering “spread” over the entire skyline, with k points. In this work, we take a more principled approach in defining the representative skyline objective. One of our main contributions is to formulate the problem of displaying k representative skyline points such that the probability that a random user would click on one of them is maximized. Two major research questions arise naturally from this formulation. First, how does one mathematically model the likelihood with which a user is interested in and will "click" on a certain tuple? Second, how does one negotiate the absence of the knowledge of an explicit set of target users; in particular what do we mean by "a random user"? To answer the first question, we model users based on a novel formulation of threshold preferences which we will motivate further in the paper. To answer the second question, we assume a probability distribution of users instead of a fixed set of users. While this makes the problem harder, it lends more mathematical structures that can be exploited as well, as one can now work with probabilities of thresholds and handle cumulative density functions. On the theoretical front, our objective is NP-hard. For the case of a finite set of users with known thresholds, we present a simple greedy algorithm that attains an approximation ratio of (1 - 1/e) of the optimal. For the case of user distributions, we show that a careful yet similar greedy algorithm achieves the same approximation ratio. Unfortunately, it turns out that this algorithm is rather involved and computationally expensive. So we present a threshold sampling based algorithm that is more computationally affordable and, for any fixed ∈ >; 0, has an approximation ratio of (1 - 1/e - ∈). We perform experiments on both real and synthetic data to show that our algorithm significantly outperforms previously proposed approaches.

In today's Internet applications or sensor networks we often encounter large amounts of data spread over many physically distributed nodes. The sheer volume of the data and bandwidth constraints make it impractical to send all the data to one central node for query processing. Finding distributed icebergs—elements that may have low frequency at individual nodes but high aggregate frequency—is a problem that arises commonly in practice. In this paper we present a novel algorithm with two notable properties. First, its accuracy guarantee and communication cost are independent of the way in which element counts (for both icebergs and non-icebergs) are split amongst the nodes. Second, it works even when each distributed data set is a stream (i.e., one pass data access only). Our algorithm builds upon sketches constructed for the estimation of the second frequency moment (F2) of data streams. The intuition of our idea is that when there are global icebergs in the union of these data streams the F2of the union becomes very large. This quantity can be estimated due to the summable nature of F2sketches. Our key innovation here is to establish tight theoretical guarantees of our algorithm, under certain reasonable assumptions, using an interesting combination of convex ordering theory and large deviation techniques.

We propose the k -representative regret minimization query ( k -regret) as an operation to support multi-criteria decision making. Like top- k , the k -regret query assumes that users have some utility or scoring functions; however, it never asks the users to provide such functions. Like skyline, it filters out a set of interesting points from a potentially large database based on the users' criteria; however, it never overwhelms the users by outputting too many tuples. In particular, for any number k and any class of utility functions, the k -regret query outputs k tuples from the database and tries to minimize the maximum regret ratio . This captures how disappointed a user could be had she seen k representative tuples instead of the whole database. We focus on the class of linear utility functions, which is widely applicable. The first challenge of this approach is that it is not clear if the maximum regret ratio would be small, or even bounded. We answer this question affirmatively. Theoretically, we prove that the maximum regret ratio can be bounded and this bound is independent of the database size. Moreover, our extensive experiments on real and synthetic datasets suggest that in practice the maximum regret ratio is reasonably small. Additionally, algorithms developed in this paper are practical as they run in linear time in the size of the database and the experiments show that their running time is small when they run on top of the skyline operation which means that these algorithm could be integrated into current database systems.

It has been well recognized that identifying very large flows (i.e., elephants) in a network traffic stream is important for a variety of network applications ranging from traffic engineering to anomaly detection. However, we found that many of these applications have an increasing need to monitor not only the few largest flows (say top 20), but also all of the medium-sized flows (say top 20,000). Unfortunately, existing techniques for identifying elephant flows at high link speeds are not suitable and cannot be trivially extended for identifying the medium-sized flows. In this work, we propose a hybrid SRAM/DRAM algorithm for monitoring all elephant and medium-sized flows with strong accuracy guarantees. We employ a synopsis data structure (sketch) in SRAM to filter out small flows and preferentially sample medium and large flows to a flow table in DRAM. Our key contribution is to show how to maximize the use of SRAM and DRAM available to us by using a SRAM/DRAM hybrid data structure that can achieve more than an order of magnitude higher SRAM efficiency than previous methods. We design a quantization scheme that allows our algorithm to "read just enough" from the sketch at SRAM speed, without sacrificing much estimation accuracy. We provide analytical guarantees on the accuracy of the estimation and validate these by means of trace-driven evaluation using real- world packet traces..

Security is becoming an increasingly important QoS parameter for which network providers should provision. We focus on monitoring and detecting one type of network event, which is important for a number of security applications such as DDoS attack mitigation and worm detection, called distributed global icebergs. While previous work has concentrated on measuring local heavy-hitters using “sketches” in the non-distributed streaming case or icebergs in the non-streaming distributed case, we focus on measuring icebergs from distributed streams. Since an iceberg may be “hidden” by being distributed across many different streams, we combine a sampling component with local sketches to catch such cases. We provide a taxonomy of the existing sketches and perform a thorough study of the strengths and weaknesses of each of them, as well as the interactions between the different components, using both real and synthetic Internet trace data. Our combination of sketching and sampling is simple yet efficient in detecting global icebergs.

Recent work has led to the ability to perform space efficient, approximate counting over large vocabularies in a streaming context. Motivated by the existence of data structures of this type, we explore the computation of associativity scores, other- wise known as pointwise mutual information (PMI), in a streaming context. We give theoretical bounds showing the impracticality of perfect online PMI compu- tation, and detail an algorithm with high expected accuracy. Experiments on news articles show our approach gives high accuracy on real world data.

We consider external algorithms for skyline computation without pre-processing. Our goal is to develop an algorithm with a good worst case guarantee while performing well on average. Due to the nature of disks, it is desirable that such algorithms access the input as a stream (even if in multiple passes). Using the tools of randomness, proved to be useful in many applications, we present an efficient multi-pass streaming algorithm, RAND, for skyline computation. As far as we are aware, RAND is the first randomized skyline algorithm in the literature. RAND is near-optimal for the streaming model, which we prove via a simple lower bound. Additionally, our algorithm is distributable and can handle partially ordered domains on each attribute. Finally, we demonstrate the robustness of RAND via extensive experiments on both real and synthetic datasets. RAND is comparable to the existing algorithms in average case and additionally tolerant to simple modifications of the data, while other algorithms degrade considerably with such variation.

We present SPIRIT, a Service for Providing Infrastructure Recommendations for Information Technology. SPIRIT allows maintenance support providers for Small-to-Medium Businesses (SMBs) to recommend solutions which are standardized (SMBs usually cannot afford customized IT solutions), flexible (accommodating as much as possible the customer’s existing IT environment), and cost-effective (minimizing the cost of upgrading the customer’s environment). SPIRIT works by first aligning the customer’s IT infrastructure with a “template” describing the best practices recommended by the maintenance support provider. Then, the aligned environment can be upgraded by choosing from a standard set of well understood, highly automated (and therefore economical) options. In this paper we present the framework of our solution.

Entropy has recently gained considerable significance as an important metric for network measurement. Previous research has shown its utility in clustering traffic and detecting traffic anomalies. While measuring the entropy of the traffic observed at a single point has already been studied, an interesting open problem is to measure the entropy of the traffic between every origin-destination pair. In this paper, we propose the first solution to this challenging problem. Our sketch builds upon and extends the Lp sketch of Indyk with significant additional innovations. We present calculations showing that our data streaming algorithm is feasible for high link speeds using commodity CPU/memory at a reasonable cost. Our algorithm is shown to be very accurate in practice via simulations, using traffic traces collected at a tier-1 ISP backbone link.