Polynomial time inductive inference of cograph pattern languages from positive data

Abstract

A cograph (complement reducible graph) is a graph which can be generated by disjoint union and complement operations on graphs, starting with a single vertex graph. Cographs arise in many areas of computer science and are studied extensively. With the goal of developing an effective data mining method for graph structured data, in this paper we introduce a graph pattern expression, called a cograph pattern, which is a special type of cograph having structured variables. Firstly, we present a polynomial time matching algorithm for cograph patterns. Secondly, we give a polynomial time algorithm for obtaining a minimally generalized cograph pattern which explains given positive data. Finally, we show that the class of cograph pattern languages is polynomial time inductively inferable from positive data. © 2012 Springer-Verlag Berlin Heidelberg.