A polynomial time solvable instance of the feasible minimum cover problem

Abstract

The feasible minimum cover problem is that of finding a minimum vertex caver S for a bipartite graph G = ( X, Y, E) such that S contains no more than α vertices from X and no more than β vertices from Y, where α and β are constants such that 0 ⩽ α ⩽ ¦X¦ and 0 ⩽ β ⩽ ¦Y¦ . This problem is closely related to the problem of reconfiguring defective VLSI arrays, such as the random access memories and is known to be NP-complete. In this paper, we present a nontrivial polynomial time solvable instance of the feasible minimum cover problem that is based on the unique decomposition of a given bipartite graph into three vertex disjoint subgraphs.