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 \(740\over 739\) unless P = NP.
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Chaudhary, A. et al. (2007). Approximating the Maximum Sharing Problem. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_6
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DOI: https://doi.org/10.1007/978-3-540-73951-7_6
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