Alphabet dependence in parameterized matching
Information Processing Letters
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
Parameterized pattern matching: algorithms and applications
Journal of Computer and System Sciences
Parameterized Duplication in Strings: Algorithms and an Application to Software Maintenance
SIAM Journal on Computing
The string B-tree: a new data structure for string search in external memory and its applications
Journal of the ACM (JACM)
Parameterized pattern matching by Boyer-Moore-type algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The String-to-String Correction Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Faster suffix tree construction with missing suffix links
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A fast algorithm for computing longest common subsequences
Communications of the ACM
Faster algorithms for the construction of parameterized suffix trees
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Approximate parameterized matching
ACM Transactions on Algorithms (TALG)
Two dimensional parameterized matching
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Information Sciences: an International Journal
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The well-known problem of the longest common subsequence (LCS), of two strings of lengths n and m respectively, is O(nm)-time solvable and is a classical distance measure for strings. Another well-studied string comparison measure is that of parameterized matching, where two equal-length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection. All works associated with parameterized pattern matching present polynomial time algorithms. There have been several attempts to accommodate parameterized matching along with other distance measures, as these turn out to be natural problems, e.g., Hamming distance, and a bounded version of edit-distance. Several algorithms have been proposed for these problems. In this paper we consider the longest common parameterized subsequence problem which combines the LCS measure with parameterized matching. We prove that the problem is NP-hard, and then show a couple of approximation algorithms for the problem.