Exact and approximation algorithms for the inversion distance between two chromosomes

John Kececioglu, David Sankoff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

68 Scopus citations

Abstract

Motivated by the problem in computational biology of reconstructing the series of chromosome inversions by which one organism evolved from another, we consider the proble m of computing the shortest series of reversals that transform one permutation to another, The permutations describe the order of genes on corresponding chromosomes, and a reversal takes an arbitrary substring of elements and reverses their order. For this problem we develop two algorithms: a greedy approximation algorithm that finds a solution provably close to optimal in O(n 2) time and O(n) space for an n element permutation, and a branch and bound exact algorithm that finds an optimal solution in O(mL(n, n)) time and O(n 2) space, where m is the size of the branch and bound search tree and L(n, n) is the time to solve a linear program of n variables and n constraints. The greedy algorithm is the first to come within a constant factor of the optimum, and guarantees a solution that uses no more than twice the minimum number of reversals. The lower and upper bounds of the branch and bound algorithm are a novel application of maximum weight matehings, shortest paths, and linear programming. In a series of experiments we study the performance of an implementation. For random permutations we find that the average difference between the upper and lower bounds is less than 3 reversals for n ≤ 50. Due to the tightness of these bounds we can solve to optimality random permutations on 30 elements in a few minutes of computer time.

Original languageEnglish (US)
Title of host publicationCombinatorial Pattern Matching - 4th Annual Symposium, CPM 1993, Proceedings
EditorsAlberto Apostolico, Alberto Apostolico, Maxime Crochemore , Zvi Galil, Zvi Galil, Udi Manber
PublisherSpringer-Verlag
Pages87-105
Number of pages19
ISBN (Print)9783540567646
DOIs
StatePublished - Jan 1 1993
Externally publishedYes
EventConference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2017 and 16th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN 2017 - Warsaw, Poland
Duration: Sep 11 2017Sep 15 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume684 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceConference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2017 and 16th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN 2017
CountryPoland
CityWarsaw
Period9/11/179/15/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kececioglu, J., & Sankoff, D. (1993). Exact and approximation algorithms for the inversion distance between two chromosomes. In A. Apostolico, A. Apostolico, M. Crochemore , Z. Galil, Z. Galil, & U. Manber (Eds.), Combinatorial Pattern Matching - 4th Annual Symposium, CPM 1993, Proceedings (pp. 87-105). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 684 LNCS). Springer-Verlag. https://doi.org/10.1007/bfb0029799