SIAM Journal on Computing
Matching patterns in strings subject to multi-linear transformations
Theoretical Computer Science
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Matching for run-length encoded strings
Journal of Complexity
Finding an o(n2 log n) Algorithm Is Sometimes Hard
Proceedings of the 8th Canadian Conference on Computational Geometry
Inplace run-length 2d compressed search
Theoretical Computer Science
A Subquadratic Sequence Alignment Algorithm for Unrestricted Scoring Matrices
SIAM Journal on Computing
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Simple deterministic wildcard matching
Information Processing Letters
Edit distance for a run-length-encoded string and an uncompressed string
Information Processing Letters
Sequence Alignment Algorithms for Run-Length-Encoded Strings
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
From coding theory to efficient pattern matching
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Efficient retrieval of approximate palindromes in a run-length encoded string
Theoretical Computer Science
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In this paper, we consider a commonly used compression scheme called run-length encoding. We provide both lower and upper bounds for the problems of comparing two run-length encoded strings. Specifically, we prove the 3sum-hardness for both the wildcard matching problem and the k-mismatch problem with run-length compressed inputs. Given two run-length encoded strings of m and n runs, such a result implies that it is very unlikely to devise an o(mn)-time algorithm for either of them. We then present an inplace algorithm running in O(mnlogm) time for their combined problem, i.e. k-mismatch with wildcards. We further demonstrate that if the aim is to report the positions of all the occurrences, there exists a stronger barrier of @W(mnlogm)-time, matching the running time of our algorithm. Moreover, our algorithm can be easily generalized to a two-dimensional setting without impairing the time and space complexity.