Years and Authors of Summarized Original Work
1996; Cole, Hariharan
2002; Farach, Hariharan, Przytycka, Thorup
Problem Definition
Consider two rooted trees T1 and T2 with n leaves each. The internal nodes of each tree have at least two children each. The leaves in each tree are labeled with the same set of labels, and further, no label occurs more than once in a particular tree. An agreement subtree of T1 and T2 is defined as follows. Let L1 be a subset of the leaves of T1 and let L2 be the subset of those leaves of T2 which have the same labels as leaves in L1. The subtree of T1induced by L1 is an agreement subtree of T1 and T2 if and only if it is isomorphic to the subtree of T2 induced by L2. The maximum agreement subtree problem (henceforth called MAST) asks for the largest agreement subtree of T1 and T2.
The terms induced subtree and isomorphism used above need to be defined. Intuitively, the subtree of T induced by a subset L of the leaves of T is the topological subtree of T...
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Recommended Reading
Amir A, Keselman D (1997) Maximum agreement subtree in a set of evolutionary trees. SIAM J Comput 26(6):1656–1669
Cole R, Hariharan R (1996) An \(O(n\log n)\) algorithm for the maximum agreement subtree problem for binary trees. In: Proceedings of 7th ACM-SIAM SODA, Atlanta, pp 323–332
Cole R, Farach-Colton M, Hariharan R, Przytycka T, Thorup M (2000) An \(O(n\log n)\) algorithm for the maximum agreement subtree problem for binary trees. SIAM J Comput 30(5):1385–1404
Farach M, Przytycka T, Thorup M (1995) The maximum agreement subtree problem for binary trees. In: Proceedings of 2nd ESA
Farach M, Przytycka T, Thorup M (1995) Agreement of many bounded degree evolutionary trees. Inf Process Lett 55(6):297–301
Farach M, Thorup M (1995) Fast comparison of evolutionary trees. Inf Comput 123(1):29–37
Farach M, Thorup M (1997) Sparse dynamic programming for evolutionary-tree comparison. SIAM J Comput 26(1):210–230
Finden CR, Gordon AD (1985) Obtaining common pruned trees. J Classific 2:255–276
Fredman ML (1975) Two applications of a probabilistic search technique: sorting X + Y and building balanced search trees. In: Proceedings of the 7th ACM STOC, Albuquerque, pp 240–244
Harel D, Tarjan RE (1984) Fast algorithms for finding nearest common ancestors. SIAM J Comput 13(2):338–355
Kao M-Y (1998) Tree contractions and evolutionary trees. SIAM J Comput 27(6):1592–1616
Kubicka E, Kubicki G, McMorris FR (1995) An algorithm to find agreement subtrees. J Classific 12:91–100
Mehlhorn K (1977) A best possible bound for the weighted path length of binary search trees. SIAM J Comput 6(2):235–239
Steel M, Warnow T (1993) Kaikoura tree theorems: computing the maximum agreement subtree. Inf Process Lett 48:77–82
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Hariharan, R. (2016). Maximum Agreement Subtree (of 2 Binary Trees). In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_220
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