Weighted Minimum-Length Rearrangement Scenarios

Authors Pijus Simonaitis , Annie Chateau, Krister M. Swenson

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Author Details

Pijus Simonaitis
  • LIRMM - Université Montpellier, France
Annie Chateau
  • LIRMM - Université Montpellier, France
Krister M. Swenson
  • LIRMM, CNRS - Université Montpellier, France

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Pijus Simonaitis, Annie Chateau, and Krister M. Swenson. Weighted Minimum-Length Rearrangement Scenarios. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We present the first known model of genome rearrangement with an arbitrary real-valued weight function on the rearrangements. It is based on the dominant model for the mathematical and algorithmic study of genome rearrangement, Double Cut and Join (DCJ). Our objective function is the sum or product of the weights of the DCJs in an evolutionary scenario, and the function can be minimized or maximized. If the likelihood of observing an independent DCJ was estimated based on biological conditions, for example, then this objective function could be the likelihood of observing the independent DCJs together in a scenario. We present an O(n⁴)-time dynamic programming algorithm solving the Minimum Cost Parsimonious Scenario (MCPS) problem for co-tailed genomes with n genes (or syntenic blocks). Combining this with our previous work on MCPS yields a polynomial-time algorithm for general genomes. The key theoretical contribution is a novel link between the parsimonious DCJ (or 2-break) scenarios and quadrangulations of a regular polygon. To demonstrate that our algorithm is fast enough to treat biological data, we run it on syntenic blocks constructed for Human paired with Chimpanzee, Gibbon, Mouse, and Chicken. We argue that the Human and Gibbon pair is a particularly interesting model for the study of weighted genome rearrangements.

Subject Classification

ACM Subject Classification
  • Applied computing → Bioinformatics
  • Weighted genome rearrangement
  • Double cut and join (DCJ)
  • Edge switch
  • Minimum-weight quadrangulation


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