Solving Classical String Problems on Compressed Texts
Abstract
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straightline programs (SLP), since all algorithms on SLPgenerated strings could be applied to processing LZcompressed texts. The main result is a new algorithm for pattern matching when both a text T and a pattern P are presented by SLPs (socalled fully compressed pattern matching problem). We show how to find a first occurrence, count all occurrences, check whether any given position is an occurrence or not in time O(n^2m). Here m,n are the sizes of straightline programs generating correspondingly P and T. Then we present polynomial algorithms for computing fingerprint table and compressed representation of all covers (for the first time) and for finding periods of a given compressed string (our algorithm is faster than previously known). On the other hand, we show that computing the Hamming distance between two SLPgenerated strings is NP and coNPhard.
 Publication:

arXiv eprints
 Pub Date:
 April 2006
 arXiv:
 arXiv:cs/0604058
 Bibcode:
 2006cs........4058L
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 E.4;
 F.2.2;
 I.7
 EPrint:
 10 pages, 6 figures, submitted