Approximate matching of run-length compressed strings

Abstract

We focus on the problem of approximate matching of strings that have been compressed using run-length encoding. Previous studies have concentrated on the problem of computing the longest common subsequence (LCS) between two strings of length m and n, compressed to m′ and n′ runs. We extend an existing algorithm for the LCS to the Levenshtein distance achieving O(m′n+n′m) complexity. This approach gives also an algorithm for approximate searching of a pattern ofm letters (m′ runs) in a text of n letters (n′ runs) in O(mm′ n′) time, both for LCS and Levenshtein models. Then we propose improvements for a greedy algorithm for the LCS, and conjecture that the improved algorithm has O(m′ n′) expected case complexity. Experimental results are provided to support the conjecture.