Matching for run-length encoded strings
Journal of Complexity
The String-to-String Correction Problem
Journal of the ACM (JACM)
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Heaviest Increasing/Common Subsequence Problems
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
A Survey of Longest Common Subsequence Algorithms
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Property matching and weighted matching
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Approximate matching in weighted sequences
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Polynomial-time approximation algorithms for weighted LCS problem
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Weighted shortest common supersequence
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
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The Longest Common Subsequence (LCS) of two strings A,B is a well studied problem having a wide range of applications. When each symbol of the input strings is assigned a positive weight the problem becomes the Heaviest Common Subsequence (HCS) problem. In this paper we consider a different version of weighted LCS on Position Weight Matrices (PWM). The Position Weight Matrix was introduced as a tool to handle a set of sequences that are not identical, yet, have many local similarities. Such a weighted sequence is a 'statistical image' of this set where we are given the probability of every symbol's occurrence at every text location. We consider two possible definitions of LCS on PWM. For the first, we solve the LCS problem of z sequences in time O(zn^z^+^1). For the second, we consider the log-probability version of the problem, prove NP-hardness and provide an approximation algorithm.