Abstract
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.
This work was supported by DFG-grant Hr 14/5-1.
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Bongartz, D. (2000). On the Approximation Ratio of the Group-Merge Algorithm for the Shortest Common Superstring Problem. In: Hlaváč, V., Jeffery, K.G., Wiedermann, J. (eds) SOFSEM 2000: Theory and Practice of Informatics. SOFSEM 2000. Lecture Notes in Computer Science, vol 1963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44411-4_18
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DOI: https://doi.org/10.1007/3-540-44411-4_18
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