# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# Maximum Compatible Tree

• Vincent Berry
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_223-2

## Years and Authors of Summarized Original Work

• 2001; Ganapathy, Warnow

## Problem Definition

This problem is a pattern matching problem on leaf-labeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a set of input trees with identical leaf sets, the goal is to find the largest subset of leaves on the branching pattern of which the input trees do not disagree. A maximum compatible tree is a tree on such a leaf set and with a branching pattern respecting that of each input tree (see below for a formal definition). The maximum compatible tree problem (MCT) is to find such a tree or, equivalently, its leaf set. The main motivation for this problem is in phylogenetics, to measure the similarity between evolutionary trees or to represent a consensus of a set of trees. The problem was introduced in [10] and [11, under the MRST acronym]. Previous related works concern the well-known maximum agreement subtree problem (MAST). Solving MASTis...

## Keywords

Consensus of trees Maximum compatible tree Pattern matching on trees Phylogenetics Trees
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## Recommended Reading

1. 1.
Berry V, Nicolas F (2006) Improved parametrized complexity of the maximum agreement subtree and maximum compatible tree problems. IEEE/ACM Trans Comput Biol Bioinformatics 3(3):289–302
2. 2.
Berry V, Nicolas F (2007) Maximum agreement and compatible supertrees. J Discret Algorithms 5(3):564–591
3. 3.
Berry V, Guillemot S, Nicolas F, Paul C (2005) On the approximation of computing evolutionary trees. In: Wang L (ed) Proceedings of the 11th annual international conference on computing and combinatorics (COCOON’05), Shanghai. LNCS, vol 3595. Springer, pp 115–125Google Scholar
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Berry V, Peng ZS, Ting HF (2008) From constrained to unconstrained maximum agreement subtree in linear time. Algorithmica 50(3):369–385
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Berry V, Guillemot S, Nicolas F, Paul C (2009) Linear time 3-approximation for the mast problem. ACM Trans. Algorithms 5(2):23:1–23:18Google Scholar
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Ganapathy G, Warnow TJ (2001) Finding a maximum compatible tree for a bounded number of trees with bounded degree is solvable in polynomial time. In: Gascuel O, Moret BME (eds) Proceedings of the 1st international workshop on algorithms in bioinformatics (WABI’01), Aarhus, pp 156–163Google Scholar
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Ganapathy G, Warnow TJ (2002) Approximating the complement of the maximum compatible subset of leaves of k trees. In: Proceedings of the 5th international workshop on approximation algorithms for combinatorial optimization (APPROX’02), Rome, pp 122–134Google Scholar
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Guillemot S, Nicolas F (2006) Solving the maximum agreement subtree and the maximum compatible tree problems on many bounded degree trees. In: Lewenshtein M, Valiente G (eds) Proceedings of the 17th combinatorial pattern matching symposium (CPM’06), Barcelona. LNCS, vol 4009. Springer, pp 165–176Google Scholar
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Hein J, Jiang T, Wang L, Zhang K (1996) On the complexity of comparing evolutionary trees. Discr Appl Math 71(1–3):153–169
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Jiang T, Wang L, Zhang K (1995) Alignment of trees – an alternative to tree edit. Theor Comput Sci 143(1):137–148
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Steel MA, Warnow TJ (1993) Kaikoura tree theorems: computing the maximum agreement subtree. Inf Process Lett 48(2):77–82
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Swofford D, Olsen G, Wadell P, Hillis D (1996) Phylogenetic inference. In: Hillis D, Moritz D, Mable B (eds) Molecular systematics, 2nd edn. Sinauer Associates, Sunderland, pp 407–514Google Scholar

## Copyright information

© Springer Science+Business Media New York 2015

## Authors and Affiliations

1. 1.Institut de Biologie ComputationnelleMontpellierFrance