Chaining algorithms for multiple genome comparison

Abstract

Given n fragments from k > 2 genomes, Myers and Miller showed how to find an optimal global chain of colinear non-overlapping fragments in O(n log k n) time and O(n log k−1 n) space. For gap costs in the L 1 -metric, we reduce the time complexity of their algorithm by a factor log 2 n log log n and the space complexity by a factor log n. For the sum-of-pairs gap cost, our algorithm improves the time complexity of their algorithm by a factor log n log log n . A variant of our algorithm finds all significant local chains of colinear non-overlapping fragments. These chaining algorithms can be used in a variety of problems in comparative genomics: the computation of global alignments of complete genomes, the identification of regions of similarity (candidate regions of conserved synteny), the detection of genome rearrangements, and exon prediction.

Novel Definition and Algorithm for Chaining Fragments with Proportional Overlaps

“…To investigate this issue, we compared the running times and coverages obtained without (using Chainer [1]) and with proportional overlaps (using Algorithm 1) on 694 pairwise genome comparisons. Our comparison set consists in all pairwise genome comparisons of strains of the same bacteria (intra-species comparisons) as of Jan 2010: it comprises 346 different genomes from 87 species retrieved from Genome Reviews database [5].…”

“…Given the set of n shared genomic intervals, i.e. fragments, the Maximum Weighted Chain problem (MWC) is solved in O(n log n) time by dynamic programming when overlaps between adjacent fragments are forbidden [10,1]. Alternatively, Felsner et al showed that this problem is a special case of the Maximum Weighted Independent Set problem in a trapezoid graph, which they solve by a sweep line algorithm over an equivalent box order representation of the graph [6].…”

“…Alternatively, Felsner et al showed that this problem is a special case of the Maximum Weighted Independent Set problem in a trapezoid graph, which they solve by a sweep line algorithm over an equivalent box order representation of the graph [6]. These algorithms [1,6] can be extended to handle fixed length overlap between adjacent fragments, but this is not sufficient to deal with the large differences in fragment length obtained even with small bacterial genomes [14]. Moreover, with those definitions the weight does not account for overlaps.…”

A graph approach to the threshold all-against-all substring matching problem

“…The chaining techniques used in [Abouelhoda and Ohlebusch 2005;Höhl et al 2002] to compute the heaviest chain are based on a graph model whose edges, in general, are a subset of the edges in G M . To prune, the authors exploit geometrical properties of their graph model, as well as a priority queue-based pruning technique.…”

Counting the number of vertex covers in a trapezoid graph

“…Trapezoid graphs are applied in various fields, including modeling channel routing problems in VLSI design [6] and identifying the optimal chain of non-overlapping fragments in bioinformatics [1]. Trapezoid graphs were first investigated in [4,6].…”