Faster Subsequence and Don\u27t-Care Pattern Matching on Compressed Texts

Subsequence pattern matching problems on compressed text were first considered by Cegielski et al. (Window Subsequence Problems for Compressed Texts, Proc. CSR 2006, LNCS 3967, pp. 127-136), where the principal problem is: given a string T represented as a straight line program (SLP) of size n, a string P of size m, compute the number of minimal subsequence occurrences of P in T. We present an O(nm) time algorithm for solving all variations of the problem introduced by Cegielski et al.. This improves the previous best known algorithm of Tiskin (Towards approximate matching in compressed strings: Local subsequence recognition, Proc. CSR 2011), which runs in O(nm log m) time. We further show that our algorithms can be modified to solve a wider range of problems in the same O(nm) time complexity, and present the first matching algorithms for patterns containing VLDC (variable length don\u27t care) symbols, as well as for patterns containing FLDC (fixed length don\u27t care) symbols, on SLP compressed texts