A New Algorithm for Subset Matching Problem

The subset matching problem is to find all occurrences of a pattern string p of length m in a text string t of length n, where each pattern and text position is a set of characters drawn from some alphabet Σ. The pattern is said to occur at text position i if the set p[j] is a subset of the set t[i + j- 1], for all j (1 ≤ j ≤ m). This is a generalization of the ordinary string matching and can be used for finding matching subtree patterns. In this research, we propose a new algorithm that needs O(n⋅m) time in the worst case. But its average time complexity is O(n + m⋅n log1.5).