Approximation algorithms for node deletion problems on bipartite graphs with finite forbidden subgraph characterization

In this paper, we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph. We look at node deletion problems for non-trivial properties which can be characterized by forbidden structure which has a bounded intersection with both the bipartitions. The approximation factors obtained directly depend upon the size of the largest such intersection. Special instances of this general problem include problems such as the Minimum Chain Vertex Deletion, Minimum Dissociation Vertex Deletion, Minimum Bipartite Claw Vertex Deletion, Minimum Bi-complement Vertex Deletion and Minimum Bipartite Threshold Vertex Deletion problems. The algorithms are based upon the techniques of linear programming and iterative rounding. We also use the node deletion algorithms to marginally improve the trivial approximation factor for complementary problem of determining the size of the maximum sized vertex induced subgraph lying in the given graph class and prove the APX-completeness of all of these problems.