Related papers: Parallel and Distributed Expander Decomposition: S…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.…
For $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities, we provide a randomized parallel algorithm for the minimum cost flow problem with $\tilde O(m+n^ {1.5})$ work and $\tilde O(\sqrt{n})$ depth. On…
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
In this paper we provide a parallel algorithm that given any $n$-node $m$-edge directed graph and source vertex $s$ computes all vertices reachable from $s$ with $\tilde{O}(m)$ work and $n^{1/2 + o(1)}$ depth with high probability in $n$ .…
In this paper, we consider networks with topologies described by some connected undirected graph ${\mathcal{G}}=(V, E)$ and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…
We present the design and analysis of a near linear-work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input of a SDD $n$-by-$n$ matrix $A$ with $m$ non-zero entries and a vector $b$, our algorithm…
In this paper we initiate the study of expander decompositions of a graph $G=(V, E)$ in the streaming model of computation. The goal is to find a partitioning $\mathcal{C}$ of vertices $V$ such that the subgraphs of $G$ induced by the…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…
We design efficient deterministic algorithms for finding short edge-disjoint paths in expanders. Specifically, given an $n$-vertex $m$-edge expander $G$ of conductance $\phi$ and minimum degree $\delta$, and a set of pairs $\{(s_i,t_i)\}_i$…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…