Generalized Substring Compression

TL;DR: This work focuses its attention on generalized substring compression and presents the first non-trivial correct algorithm for this problem and inherently proposes a method for finding the bounded longest common prefix of substrings, which may be of independent interest.

Abstract: In substring compression one is given a text to preprocess so that, upon request, a compressed substring is returned. Generalized substring compression is the same with the following twist. The queries contain an additional context substring (or a collection of context substrings) and the answers are the substring in compressed format, where the context substring is used to make the compression more efficient. We focus our attention on generalized substring compression and present the first non-trivial correct algorithm for this problem. In our algorithm we inherently propose a method for finding the bounded longest common prefix of substrings, which may be of independent interest. In addition, we propose an efficient algorithm for substring compression which makes use of range searching for minimum queries. We present several tradeoffs for both problems. For compressing the substring S [i . . j ] (possibly with the substring S [*** . . β ] as a context), best query times we achieve are O (C ) and $O\big(C\log\big(\frac{j-i}{C}\big)\big)$ for substring compression query and generalized substring compression query, respectively, where C is the number of phrases encoded.