Efficient Computation of Clustered-Clumps in Degenerate Strings

Abstract

Given a finite set of patterns, a clustered-clump is a maximal overlapping set of occurrences of such patterns. Several solutions have been presented for identifying clustered-clumps based on statistical, probabilistic, and most recently, formal language theory techniques. Here, motivated by applications in molecular biology and computer vision, we present efficient algorithms, using String Algorithm techniques, to identify clustered-clumps in a given text. The proposed algorithms compute in \(\mathcal {O}(n+m)\) time the occurrences of all clustered-clumps for a given set of degenerate patterns \(\tilde{\mathcal {P}}\) and/or degenerate text \(\tilde{T}\) of total lengths m and n, respectively; such that the total number of non-solid symbols in \(\tilde{\mathcal {P}}\) and \(\tilde{T}\) is bounded by a fixed positive integer d.