A Polynomial Time Algorithm for Finding a Minimally Generalized Linear Interval Graph Pattern

Hitoshi YAMASAKI  Takayoshi SHOUDAI 

Publication
IEICE TRANSACTIONS on Information and Systems  Vol.E92-D  No.2  pp.120-129
Publication Date: 2009/02/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science)
Category: 
Keyword: 
interval graphs,  PQ-trees,  graph structured patterns,  graph mining,  computational learning theory, 

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Summary: 
A graph is an interval graph if and only if each vertex in the graph can be associated with an interval on the real line such that any two vertices are adjacent in the graph exactly when the corresponding intervals have a nonempty intersection. A number of interesting applications for interval graphs have been found in the literature. In order to find structural features common to structural data which can be represented by intervals, this paper proposes new interval graph structured patterns, called linear interval graph patterns, and a polynomial time algorithm for finding a minimally generalized linear interval graph pattern explaining a given finite set of interval graphs.