Genome Rearrangement with ILP

The <italic>weighted Genome Sorting Problem (wGSP)</italic> is to find a minimum-weight sequence of rearrangement operations that transforms a given gene order into another given gene order using rearrangement operations that are associated with a predefined weight. This paper presents a polynomial sized Integer Linear Program -called <italic> GeRe-ILP</italic>- for solving the wGSP for the following three types of rearrangement operations: <italic>inversion </italic>, <italic>transposition</italic>, and <italic>inverse transposition</italic>. <italic>GeRe-ILP</italic> uses <inline-formula><tex-math notation="LaTeX">$O(n^3)$</tex-math><alternatives> <inline-graphic xlink:href="hartmann-ieq1-2708121.gif"/></alternatives></inline-formula> variables and <inline-formula> <tex-math notation="LaTeX">$O(n^3)$</tex-math><alternatives><inline-graphic xlink:href="hartmann-ieq2-2708121.gif"/> </alternatives></inline-formula> constraints for gene orders of length <inline-formula><tex-math notation="LaTeX">$n$ </tex-math><alternatives><inline-graphic xlink:href="hartmann-ieq3-2708121.gif"/></alternatives></inline-formula>. It is studied experimentally on simulated data how different weighting schemes influence the reconstructed scenarios. The influences of the length of the gene orders and of the size of the reconstructed scenarios on the runtime of <italic> GeRe-ILP</italic> are studied as well.

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