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

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

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.

J. Mark Keil | Jonathan Backer | J. Keil | Jonathan Backer | J. Mark Keil

[1] Wolfgang Maass,et al. Approximation schemes for covering and packing problems in image processing and VLSI , 1985, JACM.

[2] Subhash Khot,et al. Ruling out PTAS for graph min-bisection, densest subgraph and bipartite clique , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[3] Aditya Bhaskara,et al. Detecting high log-densities: an O(n¼) approximation for densest k-subgraph , 2010, STOC '10.

[4] N. Sloane,et al. Proof Techniques in Graph Theory , 1970 .

[5] Yehoshua Perl,et al. Clustering and domination in perfect graphs , 1984, Discret. Appl. Math..

[6] Jeremy P. Spinrad,et al. Modular decomposition and transitive orientation , 1999, Discret. Math..

[7] Stephan Olariu,et al. Simple Linear Time Recognition of Unit Interval Graphs , 1995, Inf. Process. Lett..

[8] Ioannis Milis,et al. A constant approximation algorithm for the densest k , 2008, Inf. Process. Lett..

[9] Brenda S. Baker,et al. Approximation algorithms for NP-complete problems on planar graphs , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).