Related papers: Fast Approximation Algorithms for Cut-based Proble…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
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 resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
We obtain faster expander decomposition algorithms for directed graphs, matching the guarantees of Saranurak and Wang (SODA 2019) for expander decomposition on undirected graphs. Our algorithms are faster than prior work and also generalize…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
We design new algorithms for approximating 2CSPs on graphs with bounded threshold rank, that is, whose normalized adjacency matrix has few eigenvalues larger than $\varepsilon$, smaller than $-\varepsilon$, or both. Unlike on worst-case…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
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…
The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…