On Approximating the Maximum Simple Sharing Problem

  • Danny Z. Chen
  • Rudolf Fleischer
  • Jian Li
  • Zhiyi Xie
  • Hong Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


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.


Bipartite Graph Maximal Solution Lower Node Path Cover Black Node 
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  1. 1.
    Antonelli, D.A., Chen, D.Z., Dysart, T.J., Hu, X.S., Khang, A.B., Kogge, P.M., Murphy, R.C., Niemier, M.T.: Quantum-dot cellular automata (QCA) circuit partitioning: problem modeling and solutions. In: Proc. 41st ACM/IEEE Design Automation Conference (DAC), pp. 363–368 (2004)Google Scholar
  2. 2.
    Berman, P., Karpinski, M.: 8/7-approximation algorithm for (1,2)-TSP. In: Proc. 17th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 2006), pp. 641–648 (2006)Google Scholar
  3. 3.
    Cao, A., Koh, C.-K.: Non-crossing OBDDs for mapping to regular circuit structures. In: Proc. IEEE International Conference on Computer Design, pp. 338–343 (2003)Google Scholar
  4. 4.
    Chaudhary, A., Chen, D.Z., Hu, X.S., Niemier, M.T., Ravinchandran, R., Whitton, K.M.: Eliminating wire crossings for molecular quantum-dot cellular automata implementation. In: Proc. IEEE/ACM International Conference on Computer-Aided Design, pp. 565–571 (2005)Google Scholar
  5. 5.
    Cook, W., Rohe, A.: Computing minimum-weight perfect matchings. INFORMS J. on Computing 11(2), 138–148 (1999)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Edmonds, J.: Maximum matching and a polyhedron with 0,1-nodes. J. Res. Nat. Bur. Stand. B 69, 125–130 (1965)MATHMathSciNetGoogle Scholar
  7. 7.
    Engebretsen, L., Karpinski, M.: TSP with bounded metrics. Journal of Computer and System Sciences 72(4), 509–546 (2006)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kosaraju, S.R., Park, J.K., Stein, C.: Long tours and short superstrings. In: Proc. 35th Annual Symp. on Foundations of Computer Science (FOCS 1994), pp. 166–177 (1994)Google Scholar
  9. 9.
    Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. Wiley, New York (1990)MATHGoogle Scholar
  10. 10.
    Li, J., Chaudhary, A., Chen, D.Z., Fleischer, R., Hu, X.S., Niemier, M.T., Xie, Z., Zhu, H.: Approximating the Maximum Sharing Problem (2006) (submitted for publication)Google Scholar
  11. 11.
    Marek-Sadowska, M., Sarrafzadeh, M.: The crossing distribution problem. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 14(4), 423–433 (1995)CrossRefGoogle Scholar
  12. 12.
    Niemier, M.T., Kogge, P.M.: Exploring and exploiting wire-level pipelining in emerging technologies. In: Proc. 28th Annual International Symp. on Computer Architecture, pp. 166–177 (2001)Google Scholar
  13. 13.
    Papadimitriou, C.H., Yannakakis, M.: The Traveling Salesman Problem with distances one and two. Mathematics of Operations Research 18(1), 1–11 (1993)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Thompson, C.D.: Area-time complexity for VLSI. In: Proc. 11th Annual ACM Symp. on Theory of Computing (STOC 1979), pp. 81–88 (1979)Google Scholar
  15. 15.
    Tougaw, P.D., Lent, C.S.: Logical devices implemented using quantum cellular automata. J. of App. Phys. 75, 1818 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Danny Z. Chen
    • 1
  • Rudolf Fleischer
    • 2
  • Jian Li
    • 2
  • Zhiyi Xie
    • 2
  • Hong Zhu
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information ProcessingFudan UniversityShanghaiChina

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