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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blum, A., Jiang, T., Li, M., Tromp, J., Yannakakis, M.: Linear approximation for shortest superstrings. In: Journal of the ACM 41(4), pp. 630–647, July 1994. 298, 299, 300, 303
Gallant, J., Maier, D., Storer, J. A.: On Finding Minimal Length superstrings. In: Journal of Computer and System Sciences 20, pp. 50–58, 1980. 298, 303
Li, M.: Toward a DNA sequencing theory. In: Proc. 31st IEEE Symp. on Foundation of Computer Science, pp. 125–134, 1990. 298, 300, 303
Jiang, T., Li, M.: DNA Sequencing and String Learning. In: Mathematical Systems Theory 29, pp. 387–405, 1996. 298, 299, 300, 301, 302
Sweedyk, Z.: A 2 1/2-approximation algorithm for shortest superstring. In: SIAM Journal on Computing 29 (3), pp. 954–86, 1999. 298
Tarhio, J., Ukkonen, E.: A greedy approximation algorithm for constructing shortest common superstrings. In: Theoretical Computer Science 57, pp. 131–145, 1988. 300, 303, 305
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-44411-4_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41348-6
Online ISBN: 978-3-540-44411-4
eBook Packages: Springer Book Archive