Cross-Document Pattern Matching

Abstract

Abstract. We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem.

Full-Fledged Real-Time Indexing for Constant Size Alphabets

“…Note that the bound f ≤ 1/4 follows from the description in [12]: the data structure in [13] uses Q-heaps [6] to answer certain queries on the set of colors in constant time.…”

Fast Algorithm for Partial Covers in Words

“…As a consequence of Lemma 1 we obtain the following result. Recall that the locus of a factor v of w, given by its start and end position in w, can be found in O(log log |v|) time [21].…”

Computing Discriminating and Generic Words

“…The data structure is similar to the one from the proof of Theorem 1 in [10]. The only difference is that the data structure E(π j ) that finds a predecessor on a path π j is replaced by the structure of [11] that answers approximate predecessor queries: for any integer d, we can find a node u ∈ π j such that d ≤ weight(u) < 2d in O(1) time.…”

“…To obtain this, we consider a special variant of weighted ancestor queries problem, to which we propose an optimal solution inspired by the one proposed in [10] for a similar problem.…”

“…This is because the latter may cost up to Ω(n 2 ) time, which is prohibitive, while the number of loci is obviously O(n). On the other hand, an enumeration of the set of loci may be sufficient for many applications (possibly as a basis for further analysis, see, e.g., [10]). Note also that for the second and third problems, the additive term |P | that appears in our complexity bounds comes from locating the locus of P in GST and can be deleted if P itself is specified by its locus in GST .…”