Abstract
We study the probability distribution of genomic distance d under the hypothesis of random gene order. We interpret the random order assumption in terms of a stochastic method for constructing the alternating colour cycles in the decomposition of the bicoloured breakpoint graph. For two random genomes of length n and χ chromosomes, we show that the expectation of n + χ– d is \(O(\frac{1}{2}\log\frac{n+\chi}{2\chi}+\frac{3}{2}\chi)\). We then discuss how to extend these analyses to the case where intra- and interchromosomal operations have different probabilities.
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© 2006 Springer-Verlag Berlin Heidelberg
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Xu, W., Zheng, C., Sankoff, D. (2006). Paths and Cycles in Breakpoint Graphs of Random Multichromosomal Genomes. In: Bourque, G., El-Mabrouk, N. (eds) Comparative Genomics. RCG 2006. Lecture Notes in Computer Science(), vol 4205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864127_5
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DOI: https://doi.org/10.1007/11864127_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44529-6
Online ISBN: 978-3-540-44530-2
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