Paths and Cycles in Breakpoint Graph of Random Multichromosomal Genomes

Wei Xu; Chunfang Zheng; David Sankoff

doi:10.1089/cmb.2007.a004

The Breakpoint Graph in Ciliates

Lecture Notes in Computer Science - Computational Life Sciences ◽

10.1007/11560500_12 ◽

2005 ◽

pp. 128-139 ◽

Cited By ~ 5

Author(s):

R. Brijder ◽

H. J. Hoogeboom ◽

G. Rozenberg

Keyword(s):

Breakpoint Graph

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Can a Breakpoint Graph be Decomposed into None Other Than 2-Cycles?

Frontiers in Algorithmics - Lecture Notes in Computer Science ◽

10.1007/978-3-319-39817-4_20 ◽

2016 ◽

pp. 205-214 ◽

Cited By ~ 2

Author(s):

Lianrong Pu ◽

Haitao Jiang

Keyword(s):

Breakpoint Graph

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THE DISTRIBUTION OF DISTANCES BETWEEN RANDOMLY CONSTRUCTED GENOMES: GENERATING FUNCTION, EXPECTATION, VARIANCE AND LIMITS

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720008003254 ◽

2008 ◽

Vol 06 (01) ◽

pp. 23-36 ◽

Cited By ~ 2

Author(s):

WEI XU

Keyword(s):

Probability Distribution ◽

Generating Function ◽

Chromosomal Rearrangement ◽

Genomic Distance ◽

Exact Probability ◽

Breakpoint Graph ◽

Exact Probability Distribution ◽

Number Of Cycles ◽

Linear Chromosomes ◽

Large Repertoire

Based on a large repertoire of chromosomal rearrangement operations, the genomic distance d between two genomes with χr and χb linear chromosomes, respectively, both containing the same (or orthologous) n genes or markers, is d = n + max (χr,χb) - c, where c is the number of cycles in the breakpoint graph of the two genomes. In this paper, we study the exact probability distribution of c. We derive the expectation and variance, and show that, in the limit, the expectation of d is [Formula: see text].

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An O(n3) algorithm for sorting signed genomes by reversals, transpositions, transreversals and block-interchanges

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720016400023 ◽

2016 ◽

Vol 14 (01) ◽

pp. 1640002 ◽

Cited By ~ 3

Author(s):

Shuzhi Yu ◽

Fanchang Hao ◽

Hon Wai Leong

Keyword(s):

Approximation Algorithm ◽

Large Scale ◽

Genome Rearrangement ◽

Approximation Scheme ◽

Running Time ◽

Breakpoint Graph ◽

Signed Permutations ◽

Comparison Results ◽

Bridge Structures ◽

Species Evolution

We consider the problem of sorting signed permutations by reversals, transpositions, transreversals, and block-interchanges. The problem arises in the study of species evolution via large-scale genome rearrangement operations. Recently, Hao et al. gave a 2-approximation scheme called genome sorting by bridges (GSB) for solving this problem. Their result extended and unified the results of (i) He and Chen — a 2-approximation algorithm allowing reversals, transpositions, and block-interchanges (by also allowing transversals) and (ii) Hartman and Sharan — a 1.5-approximation algorithm allowing reversals, transpositions, and transversals (by also allowing block-interchanges). The GSB result is based on introduction of three bridge structures in the breakpoint graph, the L-bridge, T-bridge, and X-bridge that models goodreversal, transposition/transreversal, and block-interchange, respectively. However, the paper by Hao et al. focused on proving the 2-approximation GSB scheme and only mention a straightforward [Formula: see text] algorithm. In this paper, we give an [Formula: see text] algorithm for implementing the GSB scheme. The key idea behind our faster GSB algorithm is to represent cycles in the breakpoint graph by their canonical sequences, which greatly simplifies the search for these bridge structures. We also give some comparison results (running time and computed distances) against the original GSB implementation.

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