Improved bounds on sorting with length-weighted reversals
Michael A. Bender,Dongdong Ge,Simai He,Haodong Hu,Ron Y. Pinter,Steven Skiena,Firas Swidan +6 more
- pp 919-928
TLDR
This work studies the problem of sorting integer sequences and permutations by length-weighted reversals, and gives polynomial-time algorithms to determine the optimal reversal sequence for a restricted but interesting class of sequences and cost functions.Abstract:
We study the problem of sorting integer sequences and permutations by length-weighted reversals. We consider a wide class of cost functions, namely f(l) = lα for all α ≥ 0, where l is the length of the reversed subsequence. We present tight or nearly tight upper and lower bounds on the worst-case cost of sorting by reversals. Then we develop algorithms to approximate the optimal cost to sort a given input. Furthermore, we give polynomial-time algorithms to determine the optimal reversal sequence for a restricted but interesting class of sequences and cost functions. Our results have direct application in computational biology to the field of comparative genomics.read more
Citations
More filters
Book ChapterDOI
Sorting by weighted reversals, transpositions, and inverted transpositions
Martin Bader,Enno Ohlebusch +1 more
TL;DR: This paper provides a 1.5-approximation algorithm for sorting by weighted reversals, transpositions and inverted transposition for biologically realistic weights in order to reconstruct ancient events in the evolutionary history of organisms.
Book ChapterDOI
Advances in phylogeny reconstruction from gene order and content data.
Bernard M. E. Moret,Tandy Warnow +1 more
TL;DR: This chapter surveys recent developments in the reconstruction of phylogenies from gene order and content, focusing on their performance under various stochastic models of evolution.
Book ChapterDOI
Sorting by Length-Weighted Reversals: Dealing with Signs and Circularity
TL;DR: The main result in this paper is an optimal polynomial-time algorithm for sorting circular 0/1 sequences when the cost function is additive.
Book ChapterDOI
On the cost of interchange rearrangement in strings
TL;DR: This paper studies a generalization of the classical and well-studied problem on permutations by considering general strings input, thus solving an open problem of Cayley from 1849, and examining various cost models.
Journal ArticleDOI
Improved bounds on sorting by length-weighted reversals
TL;DR: In this paper, the problem of sorting binary sequences and permutations by length-weighted reversals was studied, and polynomial-time algorithms to determine the optimal reversal sequence for a restricted but interesting class of sequences and cost functions were given.
References
More filters
The Art in Computer Programming
Andrew Hunt,Dave Thomas +1 more
TL;DR: Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.
Proceedings ArticleDOI
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
TL;DR: A duality theorem is proved explaining this intriguing performance and it is shown that there exists a “hidden” parameter that allows one to compute the reversal distance between signed permutations in polynomial time.
Journal ArticleDOI
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
TL;DR: Sorting of signed permutations by reversals is studied, a problem that adequately models rearrangements in a small genomes like chloroplast or mitochondrial DNA and proves a duality theorem explaining this intriguing performance.
Journal ArticleDOI
Lengths of chromosomal segments conserved since divergence of man and mouse.
TL;DR: Evidence is presented suggesting that chromosomal rearrangements that determine the lengths of these segments are randomly distributed within the genome.