A Further Improved Approximation Algorithm for Breakpoint Graph Decomposition

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 32 to 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 5073−15 √ 1201 3208 + ≈ 1.4193 + , for any positive . These improvements imply improved approximation results for Sorting by Reversals for almost all random permutations.