A greedy approximation algorithm for constructing shortest common superstrings
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
\boldmath A $2\frac12$-Approximation Algorithm for Shortest Superstring
SIAM Journal on Computing
Towards a DNA sequencing theory (learning a string)
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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The shortest common superstring problem (SCS) is one of the fundamental optimization problems in the area of data compression and DNA sequencing. The SCS is known to be APX-hard [1]. This paper focuses on the analysis of the approximation ratio of two greedy-based approximation algorithms for it, namely the naive Greedy algorithm and the Group-Merge algorithm. The main results of this paper are: (i) We disprove the claim that the input instances of Jiang and Li [4] prove that the Group-Merge algorithm does not provide any constant approximation for the SCS. We even prove that the Group-Merge algorithm always finds optimal solutions for these instances. (ii) We show that the Greedy algorithm and the Group-Merge algorithm are incomparable according to the approximation ratio. (iii) We attack the main problem whether the Group-Merge algorithm has a constant approximation ratio by showing that this is the case for a slightly modified algorithm denoted as Group-Merge-1 if all strings have approximately the same length and the compression is limited by a constant fraction of the trivial solution.