On approximating the maximum simple sharing problem

Authors:
Danny Z. Chen;Rudolf Fleischer;Jian Li;Zhiyi Xie;Hong Zhu
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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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.