A Further Improved Approximation Algorithm for Breakpoint Graph Decomposition

Guohui Lin and Tao Jiang
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Guohui Lin: University of Alberta
Tao Jiang: University of California

Journal of Combinatorial Optimization, 2004, vol. 8, issue 2, No 7, 183-194

Abstract: 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.

Keywords: genome rearrangement; sorting by reversals; breakpoint graph; alternating cycle decomposition; maximum independent set; k-set packing; approximation algorithm (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOCO.0000031419.12290.2b

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