Approximating the Minimum Breakpoint Linearization Problem for Genetic Maps without Gene Strandedness

TL;DR

This paper addresses the minimum breakpoint linearization problem for genetic maps without gene strandedness, proposing an approximation algorithm suitable for more realistic genetic data representations.

Contribution

It introduces a novel approximation algorithm for the MBL problem applicable to unsigned gene data, expanding the problem's practical relevance.

Findings

Algorithm achieves a ratio of (m^2+2m-1).

Runs in O(n^7) time.

Applicable to unsigned gene maps in genetic studies.

Abstract

The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint distance to a reference total order. The approximation algorithms previously developed for the MBL problem are only applicable to genetic maps in which genes or markers are represented as signed integers. However, current genetic mapping techniques generally do not specify gene strandedness so that genes can only be represented as unsigned integers. In this paper, we study the MBL problem in the latter more realistic case. An approximation algorithm is thus developed, which achieves a ratio of $(m^2+2m-1)$ and runs in $O(n^7)$ time, where $m$ is the number of genetic maps used to construct the input partial order and $n$ the total number of distinct genes in these maps.