1.375-Approximation Algorithm for Sorting by Reversals

Title1.375-Approximation Algorithm for Sorting by Reversals
Publication TypeBook Chapters
Year of Publication2002
AuthorsBerman P, Hannenhalli S, Karpinski M
EditorMöhring R, Raman R
Book TitleAlgorithms — ESA 2002Algorithms — ESA 2002
Series TitleLecture Notes in Computer Science
Pagination401 - 408
PublisherSpringer Berlin / Heidelberg
ISBN Number978-3-540-44180-9

Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals , MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.