Top-k overlapping densest subgraphs

Densest Subgraphs THE DENSE K SUBGRAPH PROBLEM

Given a graph G = (V, E) and a parameter k, we consider the problem of finding a subset U ⊆ V of size k that maximizes the number of induced edges (DkS). We improve upon the previously best known approximation ratio for DkS, a ratio that has not seen any progress during the last decade. Specifically, we improve the approximation ratio from n to n. The improved ratio is obtained by studying a va...

On Finding Densest Subgraphs and their Applications

Approximation schemes, cliques, colors and densest subgraphs

In this thesis we study the problem of finding the densest k-subgraph of a given graph G = (V, E). We present algorithms of polynomial time as well as approximation results on special graph classes. Analytically, we study polynomial time algorithms for the densest k-subgraph problem on weighted graphs of maximal degree two, on weighted trees even if the solution is disconnected, and on interval...

Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections

Dense subgraph discovery is a key issue in graph mining, due to its importance in several applications, such as correlation analysis, community discovery in the Web, gene co-expression and protein-protein interactions in bioinformatics. In this work, we study the discovery of the top-k dense subgraphs in a set of graphs. After the investigation of the problem in its static case, we extend the m...

The Densest k-Subhypergraph Problem

The Densest k-Subgraph (DkS) problem, and its corresponding minimization problem Smallest p-Edge Subgraph (SpES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed th...