On the Approximation Ratio of the Group-Merge Algorithm for the Shortest Common Superstring Problem
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 . 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  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.
Unable to display preview. Download preview PDF.
- 3.Li, M.: Toward a DNA sequencing theory. In: Proc. 31st IEEE Symp. on Foundation of Computer Science, pp. 125–134, 1990. 298, 300, 303Google Scholar