Algorithms for approximate string matching
Information and Control
An O(NP) sequence comparison algorithm
Information Processing Letters
On the inadequacy of tournament algorithms for theN-SCS problem
Information Processing Letters
Theory and algorithms for plan merging
Artificial Intelligence
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
The String-to-String Correction Problem
Journal of the ACM (JACM)
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
A fast algorithm for computing longest common subsequences
Communications of the ACM
Two Algorithms for the Longest Common Subsequence of Three (or More) Strings
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Deadlock-free routing in arbitrary networks via the flattest common supersequence method
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Online Scheduling for Sorting Buffers
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
An approximate A* algorithm and its application to the SCS problem
Theoretical Computer Science
Automatic Extraction of Process Control Flow from I/O Operations
BPM '08 Proceedings of the 6th International Conference on Business Process Management
Some Approximations for Shortest Common Nonsubsequences and Supersequences
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Improved Approximation Results on the Shortest Common Supersequence Problem
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
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It is well known that the problem of finding a shortest common supersequence (SCS) of k strings is NP-hard. In this paper we analyse four natural polynomial-time approximation algorithms for the SCS from the point of view of worst-case performance guarantee, expressed in terms of k. All four algorithms behave badly in the worst case, whether the underlying alphabet is unbounded or of fixed size. For a Tournament style algorithm proposed by Timkovsky, we show that the length of the SCS found is between (k + 2)/4 and (3k + 2)/8 times the length of the optimal in the worst case. The corresponding lower bound proved for two obvious Greedy algorithms, Greedy1 and Greedy2, is (4k + 5)/27 and the corresponding upper bounds are (k + e - 1)/e (e = 2.718...) and (k+3)/4 respectively. In the case of the so-called Majority-Merge algorithm of Jiang and Li, no worst-case guarantee beyond the trivial factor of k is possible. Even for a binary alphabet, no constant performance guarantee is possible for any of the four algorithms, in contrast with the guarantee of 2 provided by a trivial algorithm in that case.