Reversal Median Problem Research Articles

ON TWO VARIATIONS OF THE REVERSAL MEDIAN PROBLEM

We have developed an exact algorithm that solves certain instances of the Reversal Median Problem (RMP) when provided with additional input – the optimal sorting sequences between every pair of genomes. Our algorithm is able to provide an exact solution (the median genome) or determine that it is not able to do so for every instance of the problem. We have also proven the correctness of the algorithm in a theorem. RMP is the problem of finding an ancestral genome (the median) given the gene orders of three genomes. It is commonly encountered when constructing phylogeny, and is NP-hard. Two variations of the RMP were considered. In the first variation, we are given one sorting sequence for each pair of genomes. And in the second variation, we make use of a compact representation of all possible optimal sorting sequences for each pair of genomes that was developed by Braga et al.

A Hybrid Optimization Algorithm for the Multi-Chromosomal Reversal Median Problem

In this paper, we introduce a hybrid optimization algorithm with the Branch-and-Bound Method and the Ant Colony Optimization to solve the multi-chromosomal reversal median problem. We convert the large-scale genome into TSP maps at first. Then we use a hybrid optimization algorithm with the Branch-and-Bound Method and the Ant Colony Optimization to solve the problem. In our improved algorithm, we increase the search speed by implement multi-branch parallel search of ACO. Our extensive experiments on simulated datasets show that this median solver is efficient.

The transposition median problem is NP-complete

During recent years, the genomes of more and more species have been sequenced, providing data for phylogenetic reconstruction based on genome rearrangement measures, where the most important distance measures are the reversal distance and the transposition distance. The two main tasks in all phylogenetic reconstruction algorithms are to calculate pairwise distances and to solve the median of three problem. While the reversal distance problem can be solved in linear time, the reversal median problem has been proven to be NP-complete. The status of the transposition distance problem is still open, but it is conjectured to be more difficult than the reversal problem. This, in turn, also suggests that the transposition median problem is NP-complete. However, this conjecture could not yet be proven. We have now succeeded in giving a non-trivial proof for the NP-completeness of the transposition median problem.

Improving reversal median computation using commuting reversals and cycle information.

In the past decade, genome rearrangements have attracted increasing attention from both biologists and computer scientists as a new type of data for phylogenetic analysis. Methods for reconstructing phylogeny from genome rearrangements include distance-based methods, MCMC methods, and direct optimization methods. The latter, pioneered by Sankoff and extended with the software suites GRAPPA and MGR, is the most accurate approach, but is very limited due to the difficulty of its scoring procedure--it must solve multiple instances of the reversal median problem to compute the score of a given tree. The reversal median problem is known to be NP-hard and all existing solvers are extremely slow when the genomes are distant. In this paper, we present a new reversal median heuristic for unichromosomal genomes. The new method works by applying sets of reversals in a batch where all such reversals both commute and do not break the cycle of any other. Our testing using simulated datasets shows that this method is much faster than the leading solver for difficult datasets with only a slight accuracy penalty, yet retains better accuracy than other heuristics with comparable speed, and provides the additional option of searching for multiple medians. This method dramatically increases the speed of current direct optimization methods and enables us to extend the range of their applicability to organellar and small nuclear genomes with more than 50 reversals along each edge.

Solving the Preserving Reversal Median Problem

Genomic rearrangement operations can be very useful to infer the phylogenetic relationship of gene orders representing species. We study the problem of finding potential ancestral gene orders for the gene orders of given taxa, such that the corresponding rearrangement scenario has a minimal number of reversals, and where each of the reversals has to preserve the common intervals of the given input gene orders. Common intervals identify sets of genes that occur consecutively in all input gene orders. The problem of finding such an ancestral gene order is called the preserving reversal median problem (pRMP). A tree-based data structure for the representation of the common intervals of all input gene orders is used in our exact algorithm TCIP for solving the pRMP. It is known that the minimum number of reversals to transform one gene order into another can be computed in polynomial time, whereas the corresponding problem with the restriction that common intervals should not be destroyed is already NP-hard. It is shown theoretically that TCIP can solve a large class of pRMP instances in polynomial time. Empirically we show the good performance of TCIP on biological and artificial data.

Using median sets for inferring phylogenetic trees

Algorithms for phylogenetic tree reconstruction based on gene order data typically repeatedly solve instances of the reversal median problem (RMP) which is to find for three given gene orders a fourth gene order (called median) with a minimal sum of reversal distances. All existing algorithms of this type consider only one median for each RMP instance even when a large number of medians exist. A careful selection of one of the medians might lead to better phylogenetic trees. We propose a heuristic algorithm amGRP for solving the multiple genome rearrangement problem (MGRP) by repeatedly solving instances of the RMP taking all medians into account. Algorithm amGRP uses a branch-and-bound method that branches over medians from a selected subset of all medians for each RMP instance. Different heuristics for selecting the subsets have been investigated. To show that the medians for RMP vary strongly with respect to different properties that are likely to be relevant for phylogenetic tree reconstruction, the set of all medians has been investigated for artificial datasets and mitochondrial DNA (mtDNA) gene orders. Phylogenetic trees have been computed for a large set of randomly generated gene orders and two sets of mtDNA gene order data for different animal taxa with amGRP and with two standard approaches for solving the MGRP (GRAPPA-DCM and MGR). The results show that amGRP outperforms both other methods with respect to solution quality and computation time on the test data. The source code of amGRP, additional results and the test instances used in this paper are freely available from the authors.

An algorithm for reversal median problem

In this paper, we present an algorithm for reversal median problem whose performance ratio is less than 2.

The Reversal Median Problem

In this paper, we study the Reversal Median Problem (RMP), which arises in computational biology as a basic model for the reconstruction of evolutionary trees. Given q genomes, RMP calls for another genome such that the sum of the reversal distances between this genome and the given ones is minimized. So far, the problem has been considered too complex to derive mathematical models useful for its analysis and solution. We provide a powerful graph-theoretic relaxation of RMP, essentially calling for a perfect matching in a graph that forms the maximum number of cycles jointly with q given perfect matchings. By using this relaxation, we can show the complexity of RMP as well as design effective algorithms for its exact and heuristic solution. We report the solution of a few hundred instances associated with real-world genomes.