6 research outputs found
Finding Connected Dense -Subgraphs
Given a connected graph on vertices and a positive integer ,
a subgraph of on vertices is called a -subgraph in . We design
combinatorial approximation algorithms for finding a connected -subgraph in
such that its density is at least a factor
of the density of the densest -subgraph
in (which is not necessarily connected). These particularly provide the
first non-trivial approximations for the densest connected -subgraph problem
on general graphs
The densest k-subgraph problem on clique graphs
The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs, we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm for trees of cliques. © 2007 Springer Science+Business Media, LLC
The densest k-subgraph problem on clique graphs
The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs, we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm for trees of cliques