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A Further Improved Approximation Algorithm for Breakpoint Graph Decomposition

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  • Guohui Lin

    (University of Alberta)

  • Tao Jiang

    (University of California)

Abstract

Breakpoint graph decomposition is a crucial step in all recent approximation algorithms for SORTING BY REVERSALS, which is one of the best-known algorithmic problems in computational molecular biology. Caprara and Rizzi recently improved the approximation ratio for breakpoint graph decomposition from $$\frac{3}{2}$$ to $$\frac{{33}}{{23}}$$ + ∈ ≈ 1.4348 + ∈, for any positive ∈. In this paper, we extend the techniques of Caprara and Rizzi and incorporate a balancing argument to further improve the approximation ratio to $$\frac{{5073 - \sqrt {1201} }}{{3208}}$$ + ∈ ≈ 1.4193 + ∈, for any positive ∈. These improvements imply improved approximation results for SORTING BY REVERSALS for almost all random permutations.

Suggested Citation

  • Guohui Lin & Tao Jiang, 2004. "A Further Improved Approximation Algorithm for Breakpoint Graph Decomposition," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 183-194, June.
    • Handle: RePEc:spr:jcomop:v:8:y:2004:i:2:d:10.1023_b:joco.0000031419.12290.2b
    DOI: 10.1023/B:JOCO.0000031419.12290.2b
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    References listed on IDEAS

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    1. Alberto Caprara & Romeo Rizzi, 2002. "Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 157-182, June.
    2. Alberto Caprara, 1999. "On the Tightness of the Alternating-Cycle Lower Bound for Sorting by Reversals," Journal of Combinatorial Optimization, Springer, vol. 3(2), pages 149-182, July.
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    Cited by:

    1. Xin Chen, 2013. "On sorting unsigned permutations by double-cut-and-joins," Journal of Combinatorial Optimization, Springer, vol. 25(3), pages 339-351, April.

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    1. Alberto Caprara & Romeo Rizzi, 2002. "Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 157-182, June.
    2. Xin Chen, 2013. "On sorting unsigned permutations by double-cut-and-joins," Journal of Combinatorial Optimization, Springer, vol. 25(3), pages 339-351, April.

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