Approximation algorithms for maximum independent set

Develop a good approximation algorithm for the MAXIMUM INDEPENDENT SET problem on r-locally chordal graphs.

Background

The paper presents r-acyclic graph-decompositions into cliques as structural generalizations of clique trees for chordal graphs. Because independent sets intersect each clique bag in at most one vertex, these decompositions might support algorithmic methods analogous to dynamic programming on tree-decompositions.

However, the class of r-locally chordal graphs contains graphs of girth greater than r, and the MAXIMUM INDEPENDENT SET problem remains NP-hard on such graphs. The authors therefore ask whether the decomposition structure can nevertheless yield useful approximation algorithms rather than exact polynomial-time algorithms.