Indexing Circular Patterns

Abstract

This paper deals with the Circular Pattern Matching Problem (CPM). In CPM, we are interested in pattern matching between the text \(\mathcal T\) and the circular pattern \(\mathcal C(\mathcal P)\) of a given pattern \(\mathcal P = \mathcal P_1 \ldots \mathcal P_m\). The circular pattern \(\mathcal C(\mathcal P)\) is formed by concatenating \(\mathcal P_1\) to the right of \(\mathcal P_m\). We can view \(\mathcal C(\mathcal P)\) as a set of m patterns starting at positions j ∈ [1..m] and wrapping around the end and if any of these patterns matches \(\mathcal T\), we find a match for \(\mathcal C(\mathcal P)\). In this paper, we present two efficient data structures to index circular patterns. This problem has applications in pattern matching in geometric and astronomical data as well as in computer graphics and bioinformatics.