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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]

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.

We consider a random sequence of calls between nodes in a complete network with link capacities. Each call first tries the direct link. If that link is saturated, then the `first-fit dynamic alternative routing algorithm' sequentially selects up to d random two-link alternative routes, and assigns the call to the first route with spare capacity on each link, if there is such a route. The `balanced dynamic alternative routing algorithm' simultaneously selects d random two-link alternative routes; and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated. We determine the capacities needed for these algorithms to route calls successfully, and find that the second `balanced' algorithm requires a much smaller capacity. Our results strengthen and extend the discrete-time results presented in [10]. [ABSTRACT FROM AUTHOR]

We present an algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. In order to be efficient in terms of both time and space, our algorithm is based on a decomposition strategy which partitions the graph into disjoint clusters of bounded radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; most importantly, for a large family of graphs, it features a round complexity asymptotically smaller than the one exhibited by a natural approximation algorithm based on the state-of-the-art Δ -stepping SSSP algorithm, which is its only practical, linear-space competitor in the distributed setting. We complement our theoretical findings with a proof-of-concept experimental analysis on large benchmark graphs, which suggests that our algorithm may attain substantial improvements in terms of running time compared to the aforementioned competitor, while featuring, in practice, a similar approximation ratio. [ABSTRACT FROM AUTHOR]

Problem: We study the problem of identifying differentially mutated subnetworks of a large gene–gene interaction network, that is, subnetworks that display a significant difference in mutation frequency in two sets of cancer samples. We formally define the associated computational problem and show that the problem is NP-hard. Algorithm: We propose a novel and efficient algorithm, called DAMOKLE, to identify differentially mutated subnetworks given genome-wide mutation data for two sets of cancer samples. We prove that DAMOKLE identifies subnetworks with statistically significant difference in mutation frequency when the data comes from a reasonable generative model, provided enough samples are available. Experimental results: We test DAMOKLE on simulated and real data, showing that DAMOKLE does indeed find subnetworks with significant differences in mutation frequency and that it provides novel insights into the molecular mechanisms of the disease not revealed by standard methods. [ABSTRACT FROM AUTHOR]

Next-generation DNA sequencing technologies are enabling genome-wide measurements of somatic mutations in large numbers of cancer patients. A major challenge in the interpretation of these data is to distinguish functional "driver mutations" important for cancer development from random "passenger mutations." A common approach for identifying driver mutations is to find genes that are mutated at significant frequency in a large cohort of cancer genomes. This approach is confounded by the observation that driver mutations target multiple cellular signaling and regulatory pathways. Thus, each cancer patient may exhibit a different combination of mutations that are sufficient to perturb these pathways. This mutational heterogeneity presents a problem for predicting driver mutations solely from their frequency of occurrence. We introduce two combinatorial properties, coverage and exclusivity, that distinguish driver pathways, or groups of genes containing driver mutations, from groups of genes with passenger mutations. We derive two algorithms, called Dendrix, to find driver pathways de novo from somatic mutation data. We apply Dendrix to analyze somatic mutation data from 623 genes in 188 lung adenocarcinoma patients, 601 genes in 84 glioblastoma patients, and 238 known mutations in 1000 patients with various cancers. In all data sets, we find groups of genes that are mutated in large subsets of patients and whose mutations are approximately exclusive. Our Dendrix algorithms scale to whole-genome analysis of thousands of patients and thus will prove useful for larger data sets to come from The Cancer Genome Atlas (TCGA) and other large-scale cancer genome sequencing projects. [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]

Abstract: We define and study two versions of the bipartite matching problem in the framework of two-stage stochastic optimization with recourse. In one version, the uncertainty is in the second stage costs of the edges, and in the other version, the uncertainty is in the set of vertices that needs to be matched. We prove lower bounds, and analyze efficient strategies for both cases. These problems model real-life stochastic integral planning problems, such as commodity trading, reservation systems and scheduling under uncertainty. [Copyright &y& Elsevier]

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O(logn)-competitive under these various models, where n is the total number of customers. It also shows that the algorithm is O(1)-competitive with high probability and for any arrival order when customers are uniformly distributed or when they follow a distribution satisfying a smoothness property. Experimental results for a variety of scenarios indicate that the algorithm behaves extremely well in practice. [Copyright &y& Elsevier]

We model the dynamics of an ad-hoc sensor network as a continuum percolation model, and prove that a simple local-flooding technique yields an efficient communication protocol in that setting. [Copyright &y& Elsevier]

Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we present first-known, fully-distributed algorithms for the fundamental distributed agreement problem in dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our algorithms guarantee stable almost-everywhere agreement with high probability even under high adversarial churn and run in time that is polylogarithmic in n (which is the stable network size). Our first algorithm can tolerate a churn of up to εn per time step, sends only polylogarithmic number of bits per node per time step, and works under an adversary that is oblivious to the algorithm's random choices. Our second algorithm, designed for the more challenging adaptive adversary, can tolerate a churn of up to ε n . Being easy to implement, our algorithms could serve as building blocks for other non-trivial distributed computation in dynamic networks. [ABSTRACT FROM AUTHOR]

Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search engine). In distributed computing alone, PageRank vector, or more generally random walk based quantities have been used for several different applications ranging from determining important nodes, load balancing, search, and identifying connectivity structures. Surprisingly, however, there has been little work towards designing provably efficient fully-distributed algorithms for computing PageRank. The difficulty is that traditional matrix–vector multiplication style iterative methods may not always adapt well to the distributed setting owing to communication bandwidth restrictions and convergence rates. In this paper, we present fast random walk-based distributed algorithms for computing PageRanks in general graphs and prove strong bounds on the round complexity. We first present a distributed algorithm that takes O ( log ⁡ n / ϵ ) rounds with high probability on any graph (directed or undirected), where n is the network size and ϵ is the reset probability used in the PageRank computation (typically ϵ is a fixed constant). We then present a faster algorithm that takes O ( log ⁡ n / ϵ ) rounds in undirected graphs. Both of the above algorithms are scalable, as each node sends only small (polylog n ) number of bits over each edge per round. To the best of our knowledge, these are the first fully distributed algorithms for computing PageRank vector with provably efficient running time. [ABSTRACT FROM AUTHOR]

Abstract: We formulate and study a new computational model for dynamic data. In this model, the data changes gradually and the goal of an algorithm is to compute the solution to some problem on the data at each time step, under the constraint that it only has limited access to the data each time. As the data is constantly changing and the algorithm might be unaware of these changes, it cannot be expected to always output the exact right solution; we are interested in algorithms that guarantee to output an approximate solution. In particular, we focus on the fundamental problems of sorting and selection, where the true ordering of the elements changes slowly. We provide algorithms with performance close to the optimal in expectation and with high probability. [Copyright &y& Elsevier]

A major goal of cancer sequencing projects is to identify genetic alterations that determine clinical phenotypes, such as survival time or drug response. Somatic mutations in cancer are typically very diverse, and are found in different sets of genes in different patients. This mutational heterogeneity complicates the discovery of associations between individual mutations and a clinical phenotype. This mutational heterogeneity is explained in part by the fact that driver mutations, the somatic mutations that drive cancer development, target genes in cellular pathways, and only a subset of pathway genes is mutated in a given patient. Thus, pathway-based analysis of associations between mutations and phenotype are warranted. Here, we introduce an algorithm to find groups of genes, or pathways, whose mutational status is associated to a clinical phenotype without prior definition of the pathways. Rather, we find subnetworks of genes in an gene interaction network with the property that the mutational status of the genes in the subnetwork are significantly associated with a clinical phenotype. This new algorithm is built upon HotNet, an algorithm that finds groups of mutated genes using a heat diffusion model and a two-stage statistical test. We focus here on discovery of statistically significant correlations between mutated subnetworks and patient survival data. A similar approach can be used for correlations with other types of clinical data, through use of an appropriate statistical test. We apply our method to simulated data as well as to mutation and survival data from ovarian cancer samples from The Cancer Genome Atlas. In the TCGA data, we discover nine subnetworks containing genes whose mutational status is correlated with survival. Genes in four of these subnetworks overlap known pathways, including the focal adhesion and cell adhesion pathways, while other subnetworks are novel.

Perhaps the most common question that a microarray study can ask is, "Between two given biological conditions, which genes exhibit changed expression levels?" Existing methods for answering this question either generate a comparative measure based upon a static model, or take an indirect approach, first estimating absolute expression levels and then comparing the estimated levels to one another. We present a method for detecting changes in gene expression between two samples based on data from Affymetrix GeneChips. Using a library of over 200,000 known cases of differential expression, we create a learned comparative expression measure (LCEM) based on classification of probe-level data patterns as changed or unchanged. LCEM uses perfect match probe data only; mismatch probe values did not prove to be useful in this context. LCEM is particularly powerful in the case of small microarry studies, in which a regression-based method such as RMA cannot generalize, and in detecting small expression changes. At the levels of selectivity that are typical in microarray analysis, the LCEM shows a lower false discovery rate than either MAS5 or RMA trained from a single chip. When many chips are available to RMA, LCEM performs better on two out of the three data sets, and nearly as well on the third. Performance of the MAS5 log ratio statistic was notably bad on all datasets.