On Approximating the Maximum Simple Sharing Problem

In the maximum simple sharing problem (MSS), we want to compute a set of node-disjoint simple paths in an undirected bipartite graph covering as many nodes as possible of one layer of the graph, with the constraint that all paths have both endpoints in the other layer. This is a variation of the maximum sharing problem (MS) that finds important applications in the design of molecular quantum-dot cellular automata (QCA) circuits and physical synthesis in VLSI. It also generalizes the maximum weight node-disjoint path cover problem. We show that MSS is NP-complete, present a polynomial-time 5 3 -approximation algorithm, and show that it cannot be approximated with a factor better than 740 739 unless P = NP .