# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Maximum Agreement Subtree (of 2 Binary Trees)

• Ramesh  Hariharan
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_220-2

## 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 restricted to the leaves in L, with branching information relevant to Lpreserved. More formally, for any two...

## Keywords

Isomorphism Tree agreement
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1. 1.
Amir A, Keselman D (1997) Maximum agreement subtree in a set of evolutionary trees. SIAM J Comput 26(6):1656–1669
2. 2.
Cole R, Hariharan R (1996) An O(nlogn) algorithm for the maximum agreement subtree problem for binary trees. In: Proceedings of 7th ACM-SIAM SODA, Atlanta, pp 323–332Google Scholar
3. 3.
Cole R, Farach-Colton M, Hariharan R, Przytycka T, Thorup M (2000) An O(nlogn) algorithm for the maximum agreement subtree problem for binary trees. SIAM J Comput 30(5):1385–1404
4. 4.
Farach M, Przytycka T, Thorup M (1995) The maximum agreement subtree problem for binary trees. In: Proceedings of 2nd ESAGoogle Scholar
5. 5.
Farach M, Przytycka T, Thorup M (1995) Agreement of many bounded degree evolutionary trees. Inf Process Lett 55(6):297–301
6. 6.
Farach M, Thorup M (1995) Fast comparison of evolutionary trees. Inf Comput 123(1):29–37
7. 7.
Farach M, Thorup M (1997) Sparse dynamic programming for evolutionary-tree comparison. SIAM J Comput 26(1):210–230
8. 8.
Finden CR, Gordon AD (1985) Obtaining common pruned trees. J Classific 2:255–276
9. 9.
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 240–244Google Scholar
10. 10.
Harel D, Tarjan RE (1984) Fast algorithms for finding nearest common ancestors. SIAM J Comput 13(2):338–355
11. 11.
Kao M-Y (1998) Tree contractions and evolutionary trees. SIAM J Comput 27(6):1592–1616
12. 12.
Kubicka E, Kubicki G, McMorris FR (1995) An algorithm to find agreement subtrees. J Classific 12:91–100
13. 13.
Mehlhorn K (1977) A best possible bound for the weighted path length of binary search trees. SIAM J Comput 6(2):235–239
14. 14.
Steel M, Warnow T (1993) Kaikoura tree theorems: computing the maximum agreement subtree. Inf Process Lett 48:77–82