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We study the problem of finding a Hamiltonian cycle under the promise that the input graph has a minimum degree of at least $n/2$, where $n$ denotes the number of vertices in the graph. The classical theorem of Dirac states that such graphs…
We study local aggregation and graph analysis in distributed environments using the message passing model. We provide a flexible framework, where each of the nodes in a set $S$--which is a subset of all nodes in the network--can perform a…
In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter $D$ of…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
We investigate the \emph{minimum weight cycle (MWC)} problem in the $\mathsf{CONGEST}$ model of distributed computing. For undirected weighted graphs, we design a randomized algorithm that achieves a $(k+1)$-approximation, for any…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
We study distributed optimization algorithms for minimizing the average of convex functions. The applications include empirical risk minimization problems in statistical machine learning where the datasets are large and have to be stored on…
The Quantum CONGEST model is a variant of the CONGEST model, where messages consist of $O(\log(n))$ qubits. We give a general framework for implementing quantum query algorithms in Quantum CONGEST, using the concept of parallel-queries. We…
We present several results in the CONGEST model on round complexity for Replacement Paths (RPaths), Minimum Weight Cycle (MWC), and All Nodes Shortest Cycles (ANSC). We study these fundamental problems in both directed and undirected…
Graph analytics for large scale graphs has gained interest in recent years. Many graph algorithms have been designed for vertex-centric distributed graph processing frameworks to operate on large graphs with 100 M vertices and edges, using…
We provide a new constant factor approximation algorithm for the (connected) distance-$r$ dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as…
We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial…
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…
In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…