# Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

Caprara, Alberto and Rizzi, Romeo (2002) Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals. UNSPECIFIED.

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Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present, 3/2 is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known $\frac{3}{2}$ to $\frac{33}{23}+\eps$ for any $\eps>0$. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result.