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computing the quartet distance between general trees

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66 BIBLIOGRAPHY[9] Brian W. Davis, Gang Li, and William J. Murphy. Supermatrix and species tree methodsresolve phylogenetic relationships within <strong>the</strong> big cats, pan<strong>the</strong>ra (carnivora: Felidae).Molecular Phylogenetics and Evolution, 56(1):64 – 76, 2010. ISSN 1055-7903.doi: DOI:10.1016/j.ympev.2010.01.036.[10] William H. E. Day. Optimal algorithms for comparing <strong>trees</strong> with labeled leaves. Journalof Classification, 2:7–28, 1985. ISSN 0176-4268. 10.1007/BF01908061.[11] Annette Dobson. Comparing <strong>the</strong> shapes of <strong>trees</strong>. In Anne Street and Walter Wallis,editors, Combinatorial Ma<strong>the</strong>matics III, volume 452 of Lecture Notes in Ma<strong>the</strong>matics,pages 95–100. Springer Berlin / Heidelberg, 1975. 10.1007/BFb0069548.[12] George F. Estabrook, F. R. McMorris, and Christopher A. Meacham. Comparison ofundirected phylogenetic <strong>trees</strong> based on sub<strong>trees</strong> of four evolutionary units. SystematicZoology, 34(2):193–200, 1985. ISSN 00397989.[13] Thomas Mailund and Christian N. S. Pedersen. QDist-<strong>quartet</strong> <strong>distance</strong> <strong>between</strong>evolutionary <strong>trees</strong>. Bioinformatics, 20(10):1636–1637, 2004.[14] Thomas Mailund, Jesper Nielsen, and Christian N. S. Pedersen. A sub-cubic timealgorithm for <strong>computing</strong> <strong>the</strong> <strong>quartet</strong> <strong>distance</strong> <strong>between</strong> two <strong>general</strong> <strong>trees</strong>. In InternationalJoint Conferences on Bioinformatics, Systems Biology and Intelligent Computing(IJCBS), pages 565–568, 2009.[15] D. F. Robinson and L. R. Foulds. Comparison of phylogenetic <strong>trees</strong>. Ma<strong>the</strong>maticalBiosciences, 53(1-2):131–147, 1981. ISSN 0025-5564.[16] Mike A. Steel and David Penny. Distributions of tree comparison metrics-some newresults. Systematic Biology, 42(2):pp. 126–141, 1993. ISSN 10635157.[17] Martin Stig Stissing, Christian N. S. Pedersen, Thomas Mailund, Gerth Stølting Brodal,and Rolf Fagerberg. Computing <strong>the</strong> <strong>quartet</strong> <strong>distance</strong> <strong>between</strong> evolutionary<strong>trees</strong> of bounded degree. In Series on Advances in Bioinformatics and ComputationalBiology, volume 5, pages 101–110, 2007.[18] Volker Strassen. Gaussian elimination is not optimal. Numerische Ma<strong>the</strong>matik, 13:354–356, 1969. ISSN 0029-599X.[19] John Tsang. An approximation algorithm for character compatibility and fast<strong>quartet</strong>-based phylogenetic tree comparison. Master’s <strong>the</strong>sis, University of Waterloo,October 2000.

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