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.
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