An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover

The "Constraint Bipartite Vertex Cover" problem (CBVC for short) is: given a bipartite graph G with n vertices and two positive integers k 1 ; k 2 , is there a vertex cover taking at most k 1 vertices from one and at most k 2 vertices from the other vertex set of G? CBVC is NP-complete. It formalizes the spare allocation problem for reconfigurable arrays, an important problem from VLSI manufacturing. We provide the first nontrivial so-called "fixed parameter" algorithm for CBVC, running in time O(1.3999 k1+k2 +(k 1 +k 2 )n). Our algorithm is efficient and practical for small values of k 1 and k 2 , as occurring in applications