Related papers: On the Randomized Locality of Matching Problems in…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

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…

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…

In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…

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…

The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…

Local complement is a graph operation formalized by Bouchet which replaces the neighborhood of a chosen vertex with its edge-complement. This operation induces an equivalence relation on graphs; determining the size of the resulting…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…

We give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\Delta$ on $n$ vertices, for all $k \le (1-\delta)m^*(G)$, where $\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an…

We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…

Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…

We initiate the study of approximate maximum matching in the vertex partition model, for graphs subject to dynamic changes. We assume that the $n$ vertices of the graph are partitioned among $k$ players, who execute a distributed algorithm…

In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized $\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the complexity of…

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…

The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…

Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…