On the Approximation Ratio of Algorithms for Sorting by Transpositions without Using Cycle Graphs
We study the problem of sorting by transpositions, which is related to comparative genomics. Our goal is to determine how good approximation algorithms which do not rely on the cycle graph are when it comes to approximation ratios by implementing three such algorithms. We compare their theoretical approximation ratio to the experimental results obtained by running them for all permutations of up to 13 elements. Our results suggest that the approaches adopted by these algorithms are not promising alternatives in the design of approximation algorithms with low approximation ratios. Furthermore, we prove an approximation bound of 3 for a constrained version of one algorithm, and close a missing gap on the proof for the approximation ratio of another algorithm.
KeywordsApproximation Algorithm Approximation Ratio Approximation Factor Approximation Guarantee Cycle Graph
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- 6.Fertin, G., Labarre, A., Rusu, I., Tannier, E., Vialette, S.: Combinatorics of Genome Rearrangements. The MIT Press (2009)Google Scholar
- 7.Galvão, G.R., Dias, Z.: GRAAu: Genome Rearrangement Algorithm Auditor. In: Proceedings of the 4th International Conference on Bioinformatics and Computational Biology (BICoB 2012), Las Vegas, NV, USA, pp. 97–101 (2012)Google Scholar
- 8.Galvão, G.R., Dias, Z.: On the performance of sorting permutations by prefix operations. In: Proceedings of the 4th International Conference on Bioinformatics and Computational Biology (BICoB 2012), Las Vegas, NV, USA, pp. 102–107 (2012)Google Scholar
- 9.Guyer, S.A., Heath, L.S., Vergara, J.P.: Subsequence and run heuristics for sorting by transpositions. Technical Report TR-97-20, Computer Science, Virginia Polytechnic Institute and State University (1997)Google Scholar