On the Approximation Ratio of Algorithms for Sorting by Transpositions without Using Cycle Graphs

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• 作者：Gustavo Rodrigues Galv?o (1) gustavo.galvao@students.ic.unicamp.br
  Zanoni Dias (1) zanoni@ic.unicamp.br
• 刊名：Lecture Notes in Computer Science
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：7409
• 期：1
• 页码：25-36
• 全文大小：266.2 KB
• 参考文献：1. Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM Journal on Discrete Mathematics 11(2), 224–240 (1998)
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• 作者单位：1. Institute of Computing, University of Campinas, Brazil
• ISSN：1611-3349

文摘

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.