105 research outputs found
A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures
[Background]Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees. [Results]In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search. [Conclusions]The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request
An edit script for taxonomic classifications
BACKGROUND: The NCBI taxonomy provides one of the most powerful ways to navigate sequence data bases but currently users are forced to formulate queries according to a single taxonomic classification. Given that there is not universal agreement on the classification of organisms, providing a single classification places constraints on the questions biologists can ask. However, maintaining multiple classifications is burdensome in the face of a constantly growing NCBI classification. RESULTS: In this paper, we present a solution to the problem of generating modifications of the NCBI taxonomy, based on the computation of an edit script that summarises the differences between two classification trees. Our algorithms find the shortest possible edit script based on the identification of all shared subtrees, and only take time quasi linear in the size of the trees because classification trees have unique node labels. CONCLUSION: These algorithms have been recently implemented, and the software is freely available for download from
Mirroring co-evolving trees in the light of their topologies
Determining the interaction partners among protein/domain families poses hard
computational problems, in particular in the presence of paralogous proteins.
Available approaches aim to identify interaction partners among protein/domain
families through maximizing the similarity between trimmed versions of their
phylogenetic trees. Since maximization of any natural similarity score is
computationally difficult, many approaches employ heuristics to maximize the
distance matrices corresponding to the tree topologies in question. In this
paper we devise an efficient deterministic algorithm which directly maximizes
the similarity between two leaf labeled trees with edge lengths, obtaining a
score-optimal alignment of the two trees in question.
Our algorithm is significantly faster than those methods based on distance
matrix comparison: 1 minute on a single processor vs. 730 hours on a
supercomputer. Furthermore we have advantages over the current state-of-the-art
heuristic search approach in terms of precision as well as a recently suggested
overall performance measure for mirrortree approaches, while incurring only
acceptable losses in recall.
A C implementation of the method demonstrated in this paper is available at
http://compbio.cs.sfu.ca/mirrort.htmComment: 13 pages, 2 figures, Iman Hajirasouliha and Alexander Sch\"onhuth are
joint first author
Fast alignment of fragmentation trees
Motivation: Mass spectrometry allows sensitive, automated and high-throughput analysis of small molecules such as metabolites. One major bottleneck in metabolomics is the identification of āunknownā small molecules not in any database. Recently, fragmentation tree alignments have been introduced for the automated comparison of the fragmentation patterns of small molecules. Fragmentation pattern similarities are strongly correlated with the chemical similarity of the molecules, and allow us to cluster compounds based solely on their fragmentation patterns
Faster Algorithms for the Maximum Common Subtree Isomorphism Problem
The maximum common subtree isomorphism problem asks for the largest possible
isomorphism between subtrees of two given input trees. This problem is a
natural restriction of the maximum common subgraph problem, which is -hard in general graphs. Confining to trees renders polynomial time
algorithms possible and is of fundamental importance for approaches on more
general graph classes. Various variants of this problem in trees have been
intensively studied. We consider the general case, where trees are neither
rooted nor ordered and the isomorphism is maximum w.r.t. a weight function on
the mapped vertices and edges. For trees of order and maximum degree
our algorithm achieves a running time of by
exploiting the structure of the matching instances arising as subproblems. Thus
our algorithm outperforms the best previously known approaches. No faster
algorithm is possible for trees of bounded degree and for trees of unbounded
degree we show that a further reduction of the running time would directly
improve the best known approach to the assignment problem. Combining a
polynomial-delay algorithm for the enumeration of all maximum common subtree
isomorphisms with central ideas of our new algorithm leads to an improvement of
its running time from to ,
where is the order of the larger tree, is the number of different
solutions, and is the minimum of the maximum degrees of the input
trees. Our theoretical results are supplemented by an experimental evaluation
on synthetic and real-world instances
Exploiting syntactic relations for question answering
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 61-66).Recently there has been a resurgent interest in syntax-based approaches to information access, as a means of overcoming the limitations of keyword-based approaches. So far attempts to use syntax have been ad hoc, choosing to use some syntactic information but still ignoring most of the tree structure. This thesis describes the design and implementation of SMARTQA, a proof-of-concept question answering system that compares syntactic trees in a principled manner. Specifically, SMARTQA uses a tree edit-distance algorithm to calculate the similarity between unordered, unrooted syntactic trees. The general case of this problem is NP-complete; in practice, SMARTQA demonstrates that an optimized implementation of the algorithm can be feasibly used for question answering applications.by Daniel Loreto.M.Eng
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