# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Maximum Agreement Subtree (of 3 or More Trees)

• Teresa M. Przytycka
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_221-2

## Years and Authors of Summarized Original Work

1995; Farach, Przytycka, Thorup

## Problem Definition

The maximum agreement subtree problem for k trees (k-MAST) is a generalization of a similar problem for two trees (MAST). Consider a tuple of k rooted leaf-labeled trees (T1, T2… Tk). Let A = { a1, a2, … an} be the set of leaf labels. Any subset BA uniquely determines the so-called topological restriction T | B of the three T to B. Namely, T | B is the topological subtree of T spanned by all leaves labeled with elements from B and the lowest common ancestors of all pairs of these leaves. In particular, the ancestor relation in T | B is defined so that it agrees with the ancestor relation in T. A subset B of A such T1 | B, , Tk | B are isomorphic is called an agreement set.

### Problem 1 (k-MAST).

INPUT: A tuple $$\vec{T} = (T^{1},\ldots, T^{k})$$

## Keywords

Tree alignment
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## Notes

### Acknowledgements

This work was supported by the Intramural Research Program of the National Institutes of Health, National Library of Medicine.

1. 1.
Amir A, Keselman D (1997) Maximum agreement subtree in a set of evolutionary trees: metrics and efficient algorithms. SIAM J Comput 26(6):1656–1669
2. 2.
Berry V, Nicolas F (2006) Improved parameterized complexity of the maximum agreement subtree and maximum compatible tree problems. IEEE/ACM Trans Comput Biol Bioinform 3(3):289–302
3. 3.
Berry V, Guillemot S, Nicolas F, Paul C (2005) On the approximation of computing evolutionary trees. In: COCOON, Kunming, pp 115–125Google Scholar
4. 4.
Bryand D (1997) Building trees, hunting for trees, and comparing trees: theory and methods in phylogenetic analysis. Ph.D. thesis, Department of Mathematics, University of CanterburyGoogle Scholar
5. 5.
Cole R, Farach-Colton M, Hariharan R, Przytycka T, Thorup M (2001) An o(nlogn) algorithm for the maximum agreement subtree problem for binary trees. SIAM J Comput 1385–1404Google Scholar
6. 6.
Farach M, Przytycka TM, Thorup M (1995) On the agreement of many trees. Inf Process Lett 55(6):297–301
7. 7.
Finden CR, Gordon AD (1985) Obtaining common pruned trees. J Classif 2:255–276
8. 8.
Kao M-Y, Lam T-W, Sung W-K, Ting H-F (2001) An even faster and more unifying algorithm for comparing trees via unbalanced bipartite matchings. J Algorithms 40(2):212–233
9. 9.
Lee C-M, Hung L-J, Chang M-S, Tang C-Y (2004) An improved algorithm for the maximum agreement subtree problem. In: BIBE, Taichung, p 533Google Scholar
10. 10.
Przytycka TM (1998) Transforming rooted agreement into unrooted agreement. J Comput Biol 5(2):335–349
11. 11.
Steel MA, Warnow T (1993) Kaikoura tree theorems: computing the maximum agreement subtree. Inf Process Lett 48(2):77–82