Approximating the maximum sharing problem

Authors:
Amitabh Chaudhary;Danny Z. Chen;Rudolf Fleischer;Xiaobo S. Hu;Jian Li;Michael T. Niemier;Zhiyi Xie;Hong Zhu
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;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, 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, University of Notre Dame, Notre Dame, IN and College of Computing, Georgia Institute of Technology, Atlanta, GA;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:
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Year:
2007

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Abstract

In the maximum sharing problem (MS), we want to compute a set of (non-simple) paths in an undirected bipartite graph covering as many nodes as possible of the first node layer of the graph, with the constraint that all paths have both endpoints in the second node layer and no node in that layer is covered more than once. MS is equivalent to the node-duplication based crossing elimination problem (NDCE) that arises in the design of molecular quantum-dot cellular automata (QCA) circuits and the physical synthesis of BDD based regular circuit structures in VLSI design. We show that MS is NP-hard, present a polynomial-time 1.5-approximation algorithm, and show that MS cannot be approximated with a factor better than 740/739 unless P = NP.