Faster and simpler algorithm for sorting signed permutations by reversals
Haim Kaplan,Ron Shamir,Robert E. Tarjan +2 more
- 05 Jan 1997
- pp 344-351
141
TL;DR: In this paper, the authors give a quadratic algorithm for finding the minimum number of reversals needed to sort a signed permutation, which is faster than the previous algorithm of Hannenhalli and Pevzner.
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Abstract: We give a quadratic algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does not require special data structures. Our study also considerably simplifies the combinatorial structures used by the analysis. 2 refs.
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Citations
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.
706
General k-opt submoves for the Lin–Kernighan TSP heuristic
TL;DR: This paper presents an effective implementation of k-opt in LKH-2, a variant of the Lin–Kernighan TSP heuristic, and demonstrates the effectiveness of the implementation with experiments on Euclidean instances ranging from 10,000 to10,000,000 cities.
Reconstructing contiguous regions of an ancestral genome
Webb Miller,Jian Ma +1 more
TL;DR: A new method is described for predicting the ancestral order and orientation of those intervals from their observed adjacencies in modern species, and a map of an early mammalian genome is produced that accounts for 96.8% of the available human genome sequence data.
Multiple Genome Rearrangement and Breakpoint Phylogeny
David Sankoff,Mathieu Blanchette +1 more
TL;DR: This paper shows which formulations of multiple alignment have counterparts in multiple rearrangement, and proposes a branch-and-bound solution to TSP particularly suited to instances of the Travelling Salesman Problem.
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
TL;DR: A transformation from MAX-ACD to MIN-SBR is described, which is therefore shown to be NP-hard as well, answering an outstanding question which has been open for some years.
241
References
Efficiency of a Good But Not Linear Set Union Algorithm
TL;DR: It is shown that, if t(m, n) is seen as the maximum time reqmred by a sequence of m > n FINDs and n -- 1 intermixed UNIONs, then kima(m), n is shown to be related to a functional inverse of Ackermann's functmn and as very slow-growing.
Plant mitochondrial DNA evolved rapidly in structure, but slowly in sequence
TL;DR: The tempo and mode of mitochondrial DNA evolution in six species of crucifers from two genera, Brassica and Raphanus, are examined, finding the rate of rearrangements is extraordinarily faster in plant mtDNA than in cpDNA and animal mtDNA.
714
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.
706
Transforming men into mice (polynomial algorithm for genomic distance problem)
Sridhar Hannenhalli,Pavel A. Pevzner +1 more
- 23 Oct 1995
TL;DR: A duality theorem is proved which expresses the genomic distance in terms of easily computable parameters reflecting different combinatorial properties of sets of strings and leads to a polynomial time algorithm for computing most parsimonious rearrangement scenarios for human-mouse evolution.
385
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