Chapter

Algorithms and Computation

Volume 4288 of the series Lecture Notes in Computer Science pp 547-556

On Approximating the Maximum Simple Sharing Problem

  • Danny Z. ChenAffiliated withDepartment of Computer Science and Engineering, University of Notre Dame
  • , Rudolf FleischerAffiliated withDepartment of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University
  • , Jian LiAffiliated withDepartment of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University
  • , Zhiyi XieAffiliated withDepartment of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University
  • , Hong ZhuAffiliated withDepartment of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University

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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.