Related papers: Simple linear algorithms for mining graph cores
In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…
In the $\ell$-Component Order Connectivity problem ($\ell \in \mathbb{N}$), we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S\subseteq V(G)$ such that…
Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…
Core decomposition is a fundamental graph problem with a large number of applications. Most existing approaches for core decomposition assume that the graph is kept in memory of a machine. Nevertheless, many real-world graphs are big and…
The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the…
Given a graph $G = (V, E)$ and an integer $k$, we study $k$-Vertex Seperator (resp. $k$-Edge Separator), where the goal is to remove the minimum number of vertices (resp. edges) such that each connected component in the resulting graph has…
Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many…
We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\cal…
The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC…
Finding a smallest subgraph that is k-edge-connected, or augmenting a k-edge-connected graph with a smallest subset of given candidate edges to become (k+1)-edge-connected, are among the most fundamental Network Design problems. They are…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for…
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…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…
In a (parameterized) graph edge modification problem, we are given a graph $G$, an integer $k$ and a (usually well-structured) class of graphs $\mathcal{G}$, and ask whether it is possible to transform $G$ into a graph $G' \in \mathcal{G}$…
This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…
In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A…
We consider the problem of enumerating optimal solutions for two hypergraph $k$-partitioning problems -- namely, Hypergraph-$k$-Cut and Minmax-Hypergraph-$k$-Partition. The input in hypergraph $k$-partitioning problems is a hypergraph…