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Faster exact computation of rSPR distance

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Abstract

Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees. The rooted subtree prune and regraft (rSPR) distance of the two trees has been used for this purpose, and many algorithms and software tools have been developed for computing the rSPR distance of two given phylogenetic trees. The previously fastest exact algorithm for this problem runs in \(O\left( 2.415^dn\right) \) time, where \(n\) and \(d\) are the number of leaves and the rSPR distance of the input trees, respectively. In this paper, we present a faster exact algorithm which runs in \(O\left( 2.344^dn\right) \) time. Our experiments show that the new algorithm is significantly faster than the newest version (namely, v1.1.1) of the previously best software (namely, rSPR) for RSPR distance.

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Notes

  1. In other words, we can use a similar argument of Whidden et al. (2010) to prove the correctness of the processing of \(T_1\) and \(F_2\) in this case.

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Acknowledgments

Zhi-Zhong Chen was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 24500023. Lusheng Wang was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 121608].

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Authors and Affiliations

  1. Division of Information System Design, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 359-0394, Japan

    Zhi-Zhong Chen

  2. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR

    Ying Fan & Lusheng Wang

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  1. Zhi-Zhong Chen
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  2. Ying Fan
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Correspondence to Zhi-Zhong Chen.

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Chen, ZZ., Fan, Y. & Wang, L. Faster exact computation of rSPR distance. J Comb Optim 29, 605–635 (2015). https://doi.org/10.1007/s10878-013-9695-8

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  • DOI: https://doi.org/10.1007/s10878-013-9695-8

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