Pattern matching with address errors: Rearrangement distances

Amir, Amihood; Aumann, Yonatan; Benson, Gary; Levy, Avivit; Lipsky, Ohad; Porat, Ely; Skiena, Steven; Vishne, Uzi

doi:10.1016/j.jcss.2009.03.001

Cited by 36 publications

(55 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other works [18,9,14,21,13,5] aim at computing bounds on the transposition distance of a permutation. Studies have also been devoted to variants of this problem, by considering, for example, prefix transpositions [12,22,7] (in which one of the blocks has to be a prefix of the sequence), or distance between strings [10,11,25,24,20] (where multiple occurrences of each element are allowed in the sequences), possibly with weighted or prefix transpositions [23,6,1,2,7]. Note also that sorting a permutation by block-interchanges (i.e.…”

Section: Introductionmentioning

confidence: 99%

Sorting by Transpositions Is Difficult

Bulteau

Fertin

Rusu

2011

Automata, Languages and Programming

View full text Add to dashboard Cite

Abstract.In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the SORTING BY TRANSPOSITIONS problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the SORTING BY TRANSPOSITIONS problem is NP-hard. As a corollary of our result, we also prove that the following problem from [9] is NP-hard: given a permutation π, is it possible to sort π using d b (π)/3 permutations, where d b (π) is the number of breakpoints of π?

show abstract

Section: Introductionmentioning

confidence: 99%

Sorting by Transpositions Is Difficult

Bulteau

Fertin

Rusu

2011

Automata, Languages and Programming

View full text Add to dashboard Cite

show abstract

“…To illustrate our framework for efficiently solving "similar-on-average" median problems, we use the Swap Median Permutation problem (SMP for short) as a running example. 3 Herein, the combinatorial objects are permutations over the set {e 1 , . .…”

Section: Introductionmentioning

confidence: 99%

“…The computation of the swap distance between two permutations can be carried out in O(nm) time [3] by exploiting the tight relation between swap distances and permutation cycles of permutations. Given two permutations π 1 and π 2 of a set U , a permutation cycle of π 1 with respect to π 2 is a subset of π 1 whose elements, compared to π 2 , trade positions in a circular fashion.…”

Section: Introductionmentioning

confidence: 99%

“…With respect to π 2 , the cycle representation of π 1 as a product of disjoint permutation cycles is unique (up to the ordering of the cycles). The central observation behind the swap distance computation made by Amir et al [3] is as follows: The swap distance between π 1 and π 2 is m − c(π 1 ), where c(π 1 ) is the number of permutation cycles in π 1 with respect to π 2 .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Average Parameterization and Partial Kernelization for Computing Medians

Betzler

Guo

Komusiewicz

et al. 2010

LATIN 2010: Theoretical Informatics

View full text Add to dashboard Cite

Abstract. We propose an effective polynomial-time preprocessing strategy for intractable median problems. Developing a new methodological framework, we show that if the input instances of generally intractable problems exhibit a sufficiently high degree of similarity between each other on average, then there are efficient exact solving algorithms. In other words, we show that the median problems Swap Median Permutation, Consensus Clustering, Kemeny Score, and Kemeny Tie Score all are fixed-parameter tractable with respect to the parameter "average distance between input objects". To this end, we develop the new concept of "partial kernelization" and identify interesting polynomial-time solvable special cases for the considered problems.

show abstract

“…Indeed, if G is a path, then the problem reduces to finding unordered occurrences of a given pattern in a given text. Unordered pattern-matching is recently receiving a lot of attention in the pattern-matching community [3][4][5], and as far as we know, this is the only paper which considers this scenario in trees, not to mention graphs.…”

Section: Graph Motifmentioning

confidence: 99%

Sharp Tractability Borderlines for Finding Connected Motifs in Vertex-Colored Graphs

Fellows

Fertin

Hermelin

et al.

Automata, Languages and Programming

View full text Add to dashboard Cite

Abstract. We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network analysis, an important area in bioinformatics. We give two positive results and three negative results that together draw sharp borderlines between tractable and intractable instances of the problem.

show abstract

Pattern matching with address errors: Rearrangement distances

Cited by 36 publications

References 25 publications

Sorting by Transpositions Is Difficult

Sorting by Transpositions Is Difficult

Average Parameterization and Partial Kernelization for Computing Medians

Sharp Tractability Borderlines for Finding Connected Motifs in Vertex-Colored Graphs

Contact Info

Product

Resources

About