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

We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…

Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…

Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…

We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic,…

We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various…

Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…

We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…

We give the first constant-factor approximation algorithm for Sparsest Cut with general demands in bounded treewidth graphs. In contrast to previous algorithms, which rely on the flow-cut gap and/or metric embeddings, our approach exploits…

This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…

We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…

The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…

We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$--dimensional sphere. We focus on the sparse regime, when the expected degree is constant independent of $d$ and $n$. We show that, when $d$ is larger than $n$…

We give a randomized algorithm that finds a minimum cut in an undirected weighted $m$-edge $n$-vertex graph $G$ with high probability in $O(m \log^2 n)$ time. This is the first improvement to Karger's celebrated $O(m \log^3 n)$ time…

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…

We study the recently introduced boolean-width of graphs. Our structural results are as follows. Firstly, we show that almost surely the boolean-width of a random graph on $n$ vertices is $O(\log^2 n)$, and it is easy to find the…

We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…