Polynomial Time Matching Algorithms for Tree-Like Structured Patterns in Knowledge Discovery

Abstract

Graphs have enough richness and flexibility to express discrete structures hidden in a large amount of data. Some searching methods utilizing graph algorithmic techniques have been developed in Knowledge Discovery. A term graph, which is one of expressions for graph-structured data, is a hypergraph whose hyperedges are regarded as variables. Although term graphs can represent complicated patterns found from structured data, it is hard to do pattern match and pattern search in them. We have been studying subclasses of term graphs, called regular term trees, which are suited for expressing tree-like structured data. In this paper, we consider a matching problem for a regular term tree t and a standard tree T, which decides whether or not there exists a tree T′ such that T′ is isomorphic to T and T′ is obtained by replacing variables in t with some trees. First we show that the matching problem for a regular term tree and a tree is NP-complete even if each variable in the regular term tree contains only 4 vertices. Next we give a polynomial time algorithm for solving the matching problem for a regular term tree and a tree of bounded degree such that the regular term tree has only variables consisting the constant number of vertices greater than one. We also report some computational experiments and compare our algorithm with a naive algorithm.