A and that of B," to find one of them, denoted by A and B', such that A is most similar to B' and the sum of the number of vertices of A and that of B' is largest. An algorithm for the LCSS problem for unrooted and unordered trees (in short, trees) and that for trees embedded in a plane (in short, Co-trees) are proposed. The time complexity of the algorithm for trees is O (max (ma, mb)2 NaNb) and that for CO-trees is O (mambNaNb), where, ma (mb) and Na (Nb) are the largest degree of a vertex of tree Ta (Tb) and the number of vertices of Ta (Tb), respectively. It is easy to modify the algorithms for enumerating all of the LCSSs for trees and CO-trees. The algorithms can be applied to structure-activity studies in chemistry and various structure comparison problems." />


The Largest Common Similar Substructure Problem

Shaoming LIU  Eiichi TANAKA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.4   pp.643-650
Publication Date: 1997/04/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
algorithm,  complexity,  common similar substructure,  distance,  similarity,  tree,  

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Summary: 
This paper discusses the largest common similar substructure (in short, LCSS) problem for trees. The problem is, for all pairs of "substructure of A and that of B," to find one of them, denoted by A and B', such that A is most similar to B' and the sum of the number of vertices of A and that of B' is largest. An algorithm for the LCSS problem for unrooted and unordered trees (in short, trees) and that for trees embedded in a plane (in short, Co-trees) are proposed. The time complexity of the algorithm for trees is O (max (ma, mb)2 NaNb) and that for CO-trees is O (mambNaNb), where, ma (mb) and Na (Nb) are the largest degree of a vertex of tree Ta (Tb) and the number of vertices of Ta (Tb), respectively. It is easy to modify the algorithms for enumerating all of the LCSSs for trees and CO-trees. The algorithms can be applied to structure-activity studies in chemistry and various structure comparison problems.