Approximate Matching of Run-Length Compressed Strings
Veli Mäkinen, Gonzalo Navarro and Esko Ukkonen
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. Furthermore, we extend this algorithm
to a weighted edit distance model, where the weights of the three basic
edit operations can be chosen arbitrarily. This approach gives
also an algorithm for approximate searching of a pattern of m letters (m'
runs) in a text of n letters (n' runs) in O(mm'n') time. 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.