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Algorithms and Implementation for Interconnection Graph Problem

  • Hongbing Fan
  • Christian Hundt
  • Yu-Liang Wu
  • Jason Ernst
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5165)

Abstract

The Interconnection Graph Problem (IGP) is to compute for a given hypergraph H = (V, R) a graph G = (V, E) with the minimum number of edges |E| such that for all hyperedges N ∈ R the subgraph of G induced by N is connected. Computing feasible interconnection graphs is basically motivated by the design of reconfigurable interconnection networks. This paper proves that IGP is NP-complete and hard to approximate even when all hyperedges of H have at most three vertices. Afterwards it presents a search tree based parameterized algorithm showing that the problem is fixed-parameter tractable when the hyperedge size of H is bounded. Moreover, the paper gives a reduction based greedy algorithm and closes with its experimental justification.

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References

  1. 1.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan Press, London (1976)Google Scholar
  2. 2.
    Betz, V., Rose, J., Marquardt, A.: Architecture and CAD for Deep-Submicron FPGAs. Kluwer-Academic Publisher, Boston (1999)Google Scholar
  3. 3.
    Lemieux, G., Lewis, D.: Design of Interconnection Networks for Programmable Logic. Kluwer-Academic Publisher, Boston (2003)Google Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  5. 5.
    Ellis, J., Fan, H., Fellows, M.: The Dominating Set Problem is Fixed Parameter Tractable for Graphs of Bounded Genus. Journal of Algorithms 52(2), 152–168 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Du, D.-Z., Ko, K.-I.: Theory of Computational Complexity. John Wiley & Sons, Chichester (2000)zbMATHGoogle Scholar
  7. 7.
    Monien, B., Speckenmeyer, E.: Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Inf. 22, 115–123 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. System Sci. 43, 425–440 (1991)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hongbing Fan
    • 1
  • Christian Hundt
    • 2
  • Yu-Liang Wu
    • 3
  • Jason Ernst
    • 4
  1. 1.Wilfrid Laurier UniversityWaterlooCanada
  2. 2.University of RostockGermany
  3. 3.The Chinese University of Hong Kong, Shatin, N.T.Hong Kong 
  4. 4.University of GuelphGuelphCanada

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