A novel algorithm for finding top-k weighted overlapping densest connected subgraphs in dual networks

Finding Connected Dense k -Subgraphs

Given a connected graph G on n vertices and a positive integer k ≤ n, a subgraph of G on k vertices is called a k-subgraph in G. We design combinatorial approximation algorithms for finding a connected ksubgraph in G such that its density is at least a factor Ω(max{n, k/n}) of the density of the densest k-subgraph in G (which is not necessarily connected). These particularly provide the first n...

Polynomial-Time Algorithm for Finding Densest Subgraphs in Uncertain Graphs

This paper studies the problem of finding the densest subgraph in an uncertain graph. Due to uncertainty in graphs, the traditional definitions of dense subgraphs are not applicable to uncertain graphs. In this paper, we introduce the expected density of an uncertain graph. Based on the expected density, we formalize the problem that, given an uncertain graph G = (V,E, P ) and a set of vertices...

On Finding Densest Subgraphs and their Applications

Finding Highly Connected Subgraphs

A popular way of formalizing clusters in networks are highly connected subgraphs, that is, subgraphs of k vertices that have edge connectivity larger than k/2 (equivalently, minimum degree larger than k/2). We examine the computational complexity of finding highly connected subgraphs. We show that the problem is NP-hard. Thus, we explore possible parameterizations, such as the solution size, nu...

Finding Connected Secluded Subgraphs

Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional P vs NP dichotomy and within parameterized complexity. The Π-Subgraph problem asks whether an input graph contains an induced subgraph on at...