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This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…
We present a self-stabilizing leader election algorithm for arbitrary networks, with space-complexity $O(\max\{\log \Delta, \log \log n\})$ bits per node in $n$-node networks with maximum degree~$\Delta$. This space complexity is…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around…
Set cover and hitting set are fundamental problems in combinatorial optimization which are well-studied in the offline, online, and dynamic settings. We study the geometric versions of these problems and present new online and dynamic…
Finding communities in graphs is one of the most well-studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single…
An open-locating-dominating set of a graph models a detection system for a facility with a possible "intruder" or a multiprocessor network with a possible malfunctioning processor. A "sensor" or "detector" is assumed to be installed at a…
The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application…
In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…
Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…
We study the online variant of the Min-Sum Set Cover (MSSC) problem, a generalization of the well-known list update problem. In the MSSC problem, an algorithm has to maintain the time-varying permutation of the list of $n$ elements, and…
Cohesive subgraph discovery in a network is one of the fundamental problems and investigated for several decades. In this paper, we propose the Overlapping Cohesive Subgraphs with Minimum degree (OCSM) problem which combines three key…
In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model. The first algorithm finds a…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
The densest subgraph problem, introduced in the 80s by Picard and Queyranne as well as Goldberg, is a classic problem in combinatorial optimization with a wide range of applications. The lowest outdegree orientation problem is known to be…