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In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is well understood, bandit problems with large strategy sets are still a topic of active investigation, motivated by practical applications, such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions that enable the design of efficient solutions. In this work, we study a general setting for the multi-armed bandit problem, in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the Lipschitz MAB problem. We present a solution for the multi-armed bandit problem in this setting. That is, for every metric space, we define an isometry invariant that bounds from below the performance of Lipschitz MAB algorithms for this metric space, and we present an algorithm that comes arbitrarily close tomeeting this bound. Furthermore, our technique gives even better results for benign payoff functions. We also address the full-feedback ("best expert") version of the problem, where after every round the payoffs from all arms are revealed. [ABSTRACT FROM AUTHOR]

Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm Greedy[d] of Azar et al. [SIAM J. Comput., 29 (1999), pp. 180-200] places each ball by probing d>1 random bins and placing the ball in the least loaded of them. With high probability, the maximum load under Greedy[d] is exponentially lower than the result when balls are placed uniformly randomly. Vöcking [J. ACM, 50 (2003), pp. 568-589] showed that a slightly asymmetric variant, Left[d], provides a further significant improvement. However, this improvement comes at the additional computational cost of imposing structure on the bins. Here, we present a fully decentralized and easy-to-implement algorithm called FirstDiff[d] that combines the simplicity of Greedy[d] and the improved balance of Left[d]. The key idea in FirstDiff[d] is to probe until a different bin size from the first observation is located and then place the ball. Although the number of probes could be quite large for some of the balls, we show that FirstDiff[d] requires only at most d probes on average per ball (in both the standard and the heavily loaded settings). Thus the number of probes is no greater than that of either Greedy[d] or Left[d]. More importantly, we show that FirstDiff[d] closely matches the improved maximum load ensured by Left[d] in both the standard and heavily loaded settings. We further provide a tight lower bound on the maximum load up to O(logloglogn) terms. We additionally give experimental data that FirstDiff[d] is indeed as good as Left[d], if not better, in practice. [ABSTRACT FROM AUTHOR]

Proposed efficient algorithms for two all-to-all communication operations in message-passing systems, namely, index and concatenation, are presented. A model of a fully connected message-passing system, in which the performance of any point-to-point communication is independent of the sender-receiver pair, is assumed. It is also assume that each processor has k > or - 1 ports. Experimental results featuring the performance funeability of index algorithms on the IBM SP-1 parallel system are presented. Also presented is a concatenation algorithm that is optimal for most values of n.

Optimal parallel steps are necessary for routing arbitrary permutations with high probability in time. One-time randomization before the execution of a computation task is insufficient for efficient communication. Log N bits of initial randomization per input, followed by log log N bits of randomization per packet, are sufficient to guarantee that t permutations are delivered in time t + log N. The effect of adding extra randomizing stages to a Butterfly network is simulated, and the results agree with the predictions.

We introduce Tiered Sampling, a novel technique for estimating the count of sparse motifs inmassive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M, which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs--sub-graph patterns--that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4-cliques, we present a method which allows generalizing Tiered Sampling to obtain high-quality estimates for the number of occurrence of any sub-graph of interest, while reducing the analysis effort due to specific properties of the pattern of interest. We present a complete analytical analysis and extensive experimental evaluation of our proposed method using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs. [ABSTRACT FROM AUTHOR]

Abstract Background Cancer sequencing projects are now measuring somatic mutations in large numbers of cancer genomes. A key challenge in interpreting these data is to distinguish driver mutations, mutations important for cancer development, from passenger mutations that have accumulated in somatic cells but without functional consequences. A common approach to identify genes harboring driver mutations is a single gene test that identifies individual genes that are recurrently mutated in a significant number of cancer genomes. However, the power of this test is reduced by: (1) the necessity of estimating the background mutation rate (BMR) for each gene; (2) the mutational heterogeneity in most cancers meaning that groups of genes (e.g. pathways), rather than single genes, are the primary target of mutations. Results We investigate the problem of discovering driver pathways, groups of genes containing driver mutations, directly from cancer mutation data and without prior knowledge of pathways or other interactions between genes. We introduce two generative models of somatic mutations in cancer and study the algorithmic complexity of discovering driver pathways in both models. We show that a single gene test for driver genes is highly sensitive to the estimate of the BMR. In contrast, we show that an algorithmic approach that maximizes a straightforward measure of the mutational properties of a driver pathway successfully discovers these groups of genes without an estimate of the BMR. Moreover, this approach is also successful in the case when the observed frequencies of passenger and driver mutations are indistinguishable, a situation where single gene tests fail. Conclusions Accurate estimation of the BMR is a challenging task. Thus, methods that do not require an estimate of the BMR, such as the ones we provide here, can give increased power for the discovery of driver genes.

As advances in technology allow for the collection, storage, and analysis of vast amounts of data, the task of screening and assessing the significance of discovered patterns is becoming a major challenge in data mining applications. In this work, we address significance in the context of frequent itemset mining. Specifically, we develop a novel methodology to identify a meaningful support threshold s* for a dataset, such that the number of itemsets with support at least s* represents a substantial deviation from what would be expected in a random dataset with the same number of transactions and the same individual item frequencies. These itemsets can then be flagged as statistically significant with a small false discovery rate. We present extensive experimental results to substantiate the effectiveness of our methodology. [ABSTRACT FROM AUTHOR]

Presents information on a study which described an approach for the stability of dynamic packet routing algorithms. Analysis of the dynamic performance of routing algorithms; Applications of general theorem to packet routing on a butterfly network; Results.

We present TRIÈST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, highquality approximations of the global and local (i.e., incident to each vertex) number of triangles in a fully dynamic graph represented as an adversarial stream of edge insertions and deletions. Our algorithms use reservoir sampling and its variants to exploit the user-specified memory space at all times. This is in contrast with previous approaches, which require hard-to-choose parameters (e.g., a fixed sampling probability) and offer no guarantees on the amount of memory they use. We analyze the variance of the estimations and show novel concentration bounds for these quantities. Our experimental results on very large graphs demonstrate that TRIÈST outperforms state-of-the-art approaches in accuracy and exhibits a small update time. [ABSTRACT FROM AUTHOR]

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations. [ABSTRACT FROM AUTHOR]

The tasks of extracting (top-K) Frequent Itemsets (FIs) and Association Rules (ARs) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High-quality approximations of FIs and ARs are sufficient for most practical uses. Sampling techniques can be used for fast discovery of approximate solutions, but works exploring this technique did not provide satisfactory performance guarantees on the quality of the approximation due to the difficulty of bounding the probability of under- or oversampling any one of an unknown number of frequent itemsets. We circumvent this issue by applying the statistical concept of Vapnik-Chervonenkis (VC) dimension to develop a novel technique for providing tight bounds on the sample size that guarantees approximation of the (top-K) FIs and ARs within user-specified parameters. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset. We analyze the VC-dimension of this range space and show that it is upper bounded by an easy-to-compute characteristic quantity of the dataset, the d-index, namely, the maximum integer d such that the dataset contains at least d transactions of length at least d such that no one of them is a superset of or equal to another. We show that this bound is tight for a large class of datasets. The resulting sample size is a significant improvement over previous known results. We present an extensive experimental evaluation of our technique on real and artificial datasets, demonstrating the practicality of our methods, and showing that they achieve even higher quality approximations than what is guaranteed by the analysis. [ABSTRACT FROM AUTHOR]

This paper considers online stochastic combinatorial optimization problems where uncertainties, i.e., which requests come and when, are characterized by distributions that can be sampled and where time constraints severely limit the number of offline optimizations which can be performed at decision time and/or in between decisions. It proposes online stochastic algorithms that combine the frameworks of online and stochastic optimization. Online stochastic algorithms differ from traditional a priori methods such as stochastic programming and Markov Decision Processes by focusing on the instance data that is revealed over time. The paper proposes three main algorithms: expectation E, consensus C, and regret R. They all make online decisions by approximating, for each decision, the solution to a multi-stage stochastic program using an exterior sampling method and a polynomial number of samples. The algorithms were evaluated experimentally and theoretically. The experimental results were obtained on three applications of different nature: packet scheduling, multiple vehicle routing with time windows, and multiple vehicle dispatching. The theoretical results show that, under assumptions which seem to hold on these, and other, applications, algorithm E has an expected constant loss compared to the offline optimal solution. Algorithm R reduces the number of optimizations by a factor | R|, where R is the number of requests, and has an expected ρ(1+ o(1)) loss when the regret gives a ρ-approximation to the offline problem. [ABSTRACT FROM AUTHOR]

We introduce the hiring problem, in which a growing company continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite different from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of decision making under uncertainty and has many possible applications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring problem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically significant modifications. We demonstrate several intriguing behaviors of the two strategies. Specifically, we show dramatic differences between hiring above the mean and above the median. We also show that both strategies are intrinsically connected to the lognormal distribution, leading to only very weak concentration results, and the marked importance of the first few hires on the overall outcome. [ABSTRACT FROM AUTHOR]

We focus in this work on an aspect of online computation that is not addressed by standard competitive analysis, namely, identifying request sequences for which nontrivial online algorithms are useful versus request sequences for which all algorithms perform equally poorly. The motivations for this work are advanced system and architecture designs which allow the operating system to dynamically allocate resources to online protocols such as prefetching and caching. To utilize these features, the operating system needs to identify data streams that can benefit from more resources. Our approach in this work is based on the relation between entropy, compression, and gambling, extensively studied in information theory. It has been shown that in some settings, entropy can either fully or at least partially characterize the expected outcome of an iterative gambling game. Our goal is to study the extent to which the entropy of the input characterizes the expected performance of online algorithms for problems that arise in computer applications. We study bounds based on entropy for three classical online problems—list accessing, prefetching, and caching. Our bounds relate the performance of the best online algorithm to the entropy, a parameter intrinsic to characteristics of the request sequence. This is in contrast to the competitive ratio parameter of competitive analysis, which quantifies the performance of the online algorithm with respect to an optimal offline algorithm. For the prefetching problem, we give explicit upper and lower bounds for the performance of the best prefetching algorithm in terms of the entropy of the request sequence. In contrast, we show that the entropy of the request sequence alone does not fully capture the performance of online list accessing and caching algorithms. [ABSTRACT FROM AUTHOR]

We study the long-term (steady state) performance of a simple, randomized, local load balancing technique under a broad range of input conditions. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and past load distribution in the network and can use this information to place the new tasks in the processors. A node can execute one job per step, and can also participate in one load balancing operation in which it can move tasks to a direct neighbor in the network. In the protocol we analyze here, a node equalizes its load with a random neighbor in the graph. Our analysis of the protocol does not assume any particular input distribution. The input is generated by an arbitrary deterministic or probabilistic adversary subject only to some weak statistical properties. For stability and expected performance of the system we adopt the stochastic adversary model of [Borodin et al., J. ACM, 48 (2001), pp. 13--38]. For high-probability bounds we introduce a more restricted input model, the strongly bounded adversary. Assuming the stochastic adversarial input model, we show that if the adversary does not trivially overload the network (i.e., there is an integer $w\geq 1$ such that the expected number of new jobs in any interval of length $w$ is bounded by $\lambda nw$ for some $\lambdaO (w + log n), and in the strongly bounded adversary model the waiting time of a task is O (w + log n) with high probability. We contrast these results with the work stealing load balancing protocol, where we show that in sparse networks, the load in the system and the waiting time can be exponential in the network size. [ABSTRACT FROM AUTHOR]

Focuses on building a low-diameter peer-to peer (P2P) computer networks. Description of the P2P protocol; Analysis of the protocol; Significance of the preferred connection component in the protocol.

The focus of this work is the computation of efficient strategies for commodity trading in a multimarket environment. In today's "global economy" commodities are often bought in one location and then sold (right away, or after some storage period) in different markets. Thus, a trading decision in one location must be based on expectations about future price curves in all other relevant markets, and on current and future storage and transportation costs. Investors try to compute a strategy that maximizes expected return, usually with some limitations on assumed risk. With standard stochastic assumptions on commodity price fluctuations, computing an optimal strategy can be modeled as a Markov decision process (MDP). However, in general, such a formulation does not lead to efficient algorithms. In this work a model for representing the multimarket trading problem is proposed and how to obtain efficient structured algorithms for computing optimal strategies is shown for a number of commonly used trading objective functions (expected net present value, mean-variance, and value at risk). [ABSTRACT FROM AUTHOR]