Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs

Authors:
Jonathan Backer;J. Mark Keil
Affiliations:
University of Saskatchewan, Department of Computer Science, 176 Thorvaldson Building, 110 Science Place, Saskatoon, SK, Canada, S7N 5C9;University of Saskatchewan, Department of Computer Science, 176 Thorvaldson Building, 110 Science Place, Saskatoon, SK, Canada, S7N 5C9
Venue:
Information Processing Letters
Year:
2010

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Abstract

The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for chordal graphs. We present 32-approximation algorithms for proper interval graphs and bipartite permutation graphs. The latter result relies on a new characterisation of bipartite permutation graphs which may be of independent interest.