Enumerating All Maximal Frequent Subtrees

Given a collection of leaf-labeled trees on a common leafset and a fraction f in (1/2,1], a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identifies FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has practical applications as a metric for tree similarity, for computing tree congruence, in detection horizontal gene transfer events and as a consensus approach. Enumerating FSTs extend the MAST problem by denition and reveal additional subtrees not displayed by MAST. This can happen in tow ways such a subtree is included in majority but not all of the input trees or such a subtree though included in all the input trees, does not have the maximum number of leaves. Further, FSTs can be enumerated on collection o ftrees having partially overlapping leafsets. MAST may not be useful here especially if the common overlap among leafsets is very low. Though very useful, the number of FSTs suffer from combinatorial explosion just a single enumeration of maximal frequent subtrees (MFSTs). A MFST is a FST that is not a subtree to any othe rFST. the set of MFSTs is a compact nonredundant summary of all FSTs and is much smaller in size. Here we tackle the novel problem of enumerating all MFSTs in collections of phylogenetic trees. We demonstrate its utility in returning larger consensus trees in comparison to MAST. The current implementation is available on the web. Disciplines Theory and Algorithms This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/cs_techreports/54 Enumerating All Maximal Frequent Subtrees Technical Report #12-01, Dept. of Computer Science, Iowa State University Akshay Deepak and David Fernández-Baca Department of Computer Science, Iowa State University, Ames, Iowa, USA Abstract. Given a collection of leaf-labeled trees on a common leafset and a fraction f ∈ ( 1 2 , 1 ] , a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identi es FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has practical applications as a metric for tree similarity, for computing tree congruence, in detection horizontal gene transfer events and as a consensus approach. Enumerating FSTs extend the MAST problem by de nition and reveal additional subtrees not displayed by MAST. This can happen in two ways such a subtree is included in majority but not all of the input trees or such a subtree though included in all the input trees, does not have the maximum number of leaves. Further, FSTs can be enumerated on collections of trees having partially overlapping leafsets. MAST may not be useful here especially if the common overlap among leafsets is very low. Though very useful, the number of FSTs su er from combinatorial explosion just a single MAST can exhibit exponentially many FSTs. This limits both the size of the trees that can be enumerated and the ability to comprehend enumerated FSTs. To overcome this, we propose enumeration of maximal frequent subtrees (MFSTs). A MFST is a FST that is not a subtree to any other FST. The set of MFSTs is a compact non-redundant summary of all FSTs and is much smaller in size. Here we tackle the novel problem of enumerating all MFSTs in collections of phylogenetic trees. We demonstrate its utility in returning larger consensus trees in comparison to MAST. The current implementation is available on the web. Given a collection of leaf-labeled trees on a common leafset and a fraction f ∈ ( 1 2 , 1 ] , a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identi es FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has practical applications as a metric for tree similarity, for computing tree congruence, in detection horizontal gene transfer events and as a consensus approach. Enumerating FSTs extend the MAST problem by de nition and reveal additional subtrees not displayed by MAST. This can happen in two ways such a subtree is included in majority but not all of the input trees or such a subtree though included in all the input trees, does not have the maximum number of leaves. Further, FSTs can be enumerated on collections of trees having partially overlapping leafsets. MAST may not be useful here especially if the common overlap among leafsets is very low. Though very useful, the number of FSTs su er from combinatorial explosion just a single MAST can exhibit exponentially many FSTs. This limits both the size of the trees that can be enumerated and the ability to comprehend enumerated FSTs. To overcome this, we propose enumeration of maximal frequent subtrees (MFSTs). A MFST is a FST that is not a subtree to any other FST. The set of MFSTs is a compact non-redundant summary of all FSTs and is much smaller in size. Here we tackle the novel problem of enumerating all MFSTs in collections of phylogenetic trees. We demonstrate its utility in returning larger consensus trees in comparison to MAST. The current implementation is available on the web.