Densest-Subgraph Approximation on Intersection Graphs

Danny Z. Chen, Rudolf Fleischer, Jian Li

Abstract: We study approximation solutions for the densest k-subgraph problem (DS-k) on several classes of intersection graphs. We adopt the concept of σ-quasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple O(σ)-approximation technique for graphs admitting such a vertex order. This concept allows us to derive constant factor approximation algorithms for DS-k on many intersection graph classes, such as chordal graphs, circular-arc graphs, claw-free graphs, line graphs of ℓ-hypergraphs, disk graphs, and the intersection graphs of fat geometric objects. We also present a PTAS for DS-k on unit disk graphs using the shifting technique.