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Efficient Algorithm for Embedding Hypergraphs in a Cycle

  • Qian-Ping Gu
  • Yong Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2913)

Abstract

The problem of Minimum Congestion Hypergraph Embedding in a Cycle (MCHEC) is to embed the hyperedges of a hypergraph as paths in a cycle such that the maximum congestion (the maximum number of paths that use any single link in the cycle) is minimized. This problem has many applications, including minimizing communication congestions in computer networks and parallel computations. The MCHEC problem is NP-hard. We give a 1.8-approximation algorithm for the problem. This improves the previous 2-approximation results. The algorithm has the optimal O(mn) time for the hypergraph with m hyperedges and n nodes.

Keywords

Hypergraph embedding in a cycle approximation algorithms communication on rings link congestion minimization 

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References

  1. 1.
    Carpenter, T., Cosares, S., Ganley, J.L., Saniee, I.: A simple approximation algorithm for two problems in circuit design. IEEE Trans. on Computers 47(11), 1310–1312 (1998)CrossRefGoogle Scholar
  2. 2.
    Frank, A., Nishizeki, T., Saito, N., Suzuki, H., Tardos, E.: Algorithms for routing around a rectangle. Discrete Applied Mathematics 40, 363–378 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ganley, J.L., Cohoon, J.P.: Minimum-congestion hypergraph embedding on a cycle. IEEE Trans. on Computers 46(5), 600–602 (1997)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Gonzalez, T.: Improved approximation algorithms for embedding hyperedges in a cycle. Information Processing Letters 67, 267–271 (1998)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Gonzalez, T., Lee, S.L.: A 1.6 approximation algorithm for routing multiterminal nets. SIAM J. on Computing 16, 669–704 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gonzalez, T., Lee, S.L.: A linear time algorithm for optimal routing around a rectangle. Journal of ACM 35(4), 810–832 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    LaPaugh, A.S.: A polynomial time algorithm for optimal routing around a rectangle. In: Proc. of the 21st Symposium on Foundations of Computer Science (FOCS 1980), pp. 282–293 (1980)Google Scholar
  8. 8.
    Lee, S.L., Ho, H.J.: Algorithms and complexity for weighted hypergraph embedding in a cycle. In: Proc. of the 1st International Symposium on Cyber World (CW 2002), pp. 70–75 (2002)Google Scholar
  9. 9.
    Sarrafzadeh, M., Preparata, F.P.: A bottom-up layout technique based on tworectangle routing. Integration: The VLSI Journal 5, 231–246 (1987)CrossRefGoogle Scholar
  10. 10.
    Okamura, H., Seymour, P.D.: Multicommodity flows in planar graphs. Journal of Combinatorial Theory, Series B 31, 75–81 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Gu, Q.P., Wang, Y.: Efficient algorithm for embedding hypergraphs in a cycle. Technical Report 2003-03, School of Computing Science, Simon Fraser University (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Qian-Ping Gu
    • 1
  • Yong Wang
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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