Related papers: Large Cuts with Local Algorithms on Triangle-Free …

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…

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 investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…

This paper presents a linear prioritized local algorithm that computes large independent sets on a random $d$-regular graph with small and fixed degree $d$. We studied experimentally the independence ratio obtained by the algorithm when $ d…

We present a local algorithm producing an independent set of expected size $0.44533n$ on large-girth 3-regular graphs and $0.40407n$ on large-girth 4-regular graphs. We also construct a cut (or bisection or bipartite subgraph) with…

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

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,…

For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…

The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…

We consider the problem of estimating the size of a maximum cut (Max-Cut problem) in a random Erd\H{o}s-R\'{e}nyi graph on $n$ nodes and $\lfloor cn \rfloor$ edges. It is shown in Coppersmith et al. ~\cite{Coppersmith2004} that the size of…

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…

The d-Cut problem is to decide if a graph has an edge cut such that each vertex has at most d neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The d-Cut problem has been studied…

We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an…

Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…

Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…

We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformly at random from such a graph has expected…