Approximate Matching for Run-Length Encoded Strings Is 3sum-Hard

Authors:
Kuan-Yu Chen;Ping-Hui Hsu;Kun-Mao Chao
Affiliations:
Department of Computer Science and Information Engineering,;Department of Computer Science and Information Engineering,;Department of Computer Science and Information Engineering, and Graduate Institute of Biomedical Electronics and Bioinformatics, and Graduate Institute of Networking and Multimedia, National Taiwa ...
Venue:
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Year:
2009

Citing 18
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Abstract

In this paper, we consider a commonly used compression scheme called run-length encoding (abbreviated rle ). We provide lower bounds for problems of approximately matching two rle strings. Specifically, we show that the wildcard matching and k -mismatches problems for rle strings are 3sum -hard. For two rle strings of m and n runs, such a result implies that it is very unlikely to devise an o (mn )-time algorithm for either problem. We then propose an O (mn + p logm )-time sweep-line algorithm for their combined problem, i.e. wildcard matching with mismatches, where p ≤ mn is the number of matched or mismatched runs. Furthermore, the problem of aligning two rle strings is also shown to be 3sum -hard.