On Approximating the Maximum Simple Sharing Problem

Abstract

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 $5\over 3$-approximation algorithm, and show that it cannot be approximated with a factor better than $740\over 739$ unless P = NP.

This work was supported in part by a grant from the Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China. The order of authors follows the international standard of alphabetic order of the last name. In China, where first-authorship is a particularly important aspect of a publication, the order of authors should be Zhiyi Xie, Jian Li, Hong Zhu, Danny Z. Chen, and Rudolf Fleischer.