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A 1.5-Approximation Algorithm for Two-Sided Scaffold Filling

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Abstract

The scaffold filling problem aims to set up the whole genomes by filling those missing genes into the scaffolds to optimize a similarity measure of genomes. A typical and frequently used measure for the similarity of two genomes is the number of common adjacencies. One-sided scaffold filling is given by a scaffold and a whole genome, and asks to fill the missing genes into that scaffold to result in such a genome that the number of common adjacencies between it and the given genome is maximized. Two-sided scaffold filling is given by two scaffolds, and asks to fill the missing genes into those two scaffolds respectively to result in such two genomes that the number of common adjacencies between them is maximized. One-sided scaffold filling can be approximated to \(\frac{5}{4}\) by now. However, the algorithmic progress for two-sided scaffold filling seems rare. What we know for two-sided scaffold filling is a 2-approximation algorithm by now. In this paper, we propose a new algorithm for two-sided scaffold filling which can achieve a performance ratio of \(\frac{3}{2}\) in \(O(N^3)\) time, where \(N\) is the number of genes in an output genome. An example can be given to show that the performance ratio \(\frac{3}{2}\) for this algorithm is actually tight.

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References

  1. Angibaud, S., Fertin, G., Rusu, I., Thevenin, A., Vialette, S.: On the approximability of comparing genomes with duplicates. J. Graph Algorithms Appl. 13(1), 19–53 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blin, G., Fertin, G., Sikora, F., Vialette, S.: The exemplar breakpoint distance for nontrivial genomes cannot be approximated. In: Proceedings of 3rd Workshop on Algorithm and Computation, LNCS 5431, pp. 357–368 (2009)

  3. Chen, Z., Fu, B., Zhu, B.: The approximability of the exemplar breakpoint distance problem. In: Proceedings of 2nd International Conference on Algorithmic Aspects in Information and Management \((AAIM^{\prime }06)\), LNCS 4041, pp. 291–302 (2006)

  4. Chen, Z., Fowler, R., Fu, B., Zhu, B.: On the inapproximability of the exemplar conserved interval distance problem of genomes. J. Comb. Optim. 15(2), 201–221 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves. In: Proceedings of 13th ACM-SIAM Symposium on Discrete Algorithms \((SODA^{\prime }02)\), pp. 667–676 (2002)

  6. Goldstein, A., Kolman, P., Zheng, J.: Minimum common string partitioning problem: hardness and approximations. In: Proceedings of 15th International Symposium on Algorithms and Computation \((ISAAC^{\prime }04)\), LNCS 3341, pp. 473–484 (2004)

  7. Huson, D.H., Reinert, K., Myers, E.W.: The greedy path-merging algorithm for contig scaffolding. J. ACM 49(5), 603–615 (2002)

    Article  MathSciNet  Google Scholar 

  8. Jiang, H., Zhong, F., Zhu, B.: Filling scaffolds with gene repetitions: maximizing the number of adjacencies. In: Proceedings of 22nd Annual Symposium on Combinatorial Pattern Matching \((CPM^{\prime }11)\), LNCS 6661, pp. 55–64 (2011)

  9. Jiang, M.: The zero exemplar distance problem. In: Proceedings of the 2010 International RECOMB-CG Workshop (RECOMB-CG’10), LNBI 6398, pp. 74–82 (2010)

  10. Jiang, H., Zheng, C., Sankoff, D., Zhu, B.: Scaffold filling under the breakpoint and related distances. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(4), 1220–1229 (2012)

    Article  Google Scholar 

  11. Liu, N., Jiang, H., Zhu, D., Zhu, B.: An improved approximation algorithm for scaffold filling to maximize the common adjacencies. In: The 19th Annual International Computing and Combinatorics Conference \((COCOON^{\prime }13)\), LNCS 7936, pp. 397–408, (2013). IEEE/ACM Trans. Comput. Biol. Bioinform., 10(4), 905–913 (2013)

  12. Liu, N., Zhu, D.: The algorithm for two-sided scaffold filling problem. In: The 10th Annual International Conference on Theory and Applications of Models of Computation \((TAMC 2013)\), LNCS 7876, pp. 236–247 (2013)

  13. Muñoz, A., Zheng, C., Zhu, Q., Albert, V., Rounsley, S., Sankoff, D.: Scaffold filling, contig fusion and gene order comparison. BMC Bioinform. 11, 304 (2010)

    Article  Google Scholar 

  14. Sankoff, D.: Genome rearrangement with gene families. Bioinformatics 15(11), 909–917 (1999)

    Article  Google Scholar 

Download references

Acknowledgments

This research is supported by the National Nature Science Foundation of China (61070019, 61202014), the Natural Science Foundation of Shandong Province (\(ZR\)-2012-\(Z002\)), and the Chinese Postdoctoral Science Foundation (2011-\(M\)-501133, 2012-\(T\)-50614).

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Correspondence to Daming Zhu.

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Liu, N., Zhu, D., Jiang, H. et al. A 1.5-Approximation Algorithm for Two-Sided Scaffold Filling. Algorithmica 74, 91–116 (2016). https://doi.org/10.1007/s00453-014-9938-9

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  • DOI: https://doi.org/10.1007/s00453-014-9938-9

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