Inapproximability of Maximal Strip Recovery: II

  • Minghui Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)


Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given d genomic maps as sequences of gene markers, the objective of MSR-d is to find d subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. In our recent paper entitled “Inapproximability of Maximal Strip Recovery” in ISAAC 2009, we proved that MSR-d is APX-hard for any constant d ≥ 2, and presented the first explicit lower bounds for approximating MSR-2, MSR-3, andMSR-4, even for the most basic version of the problem in which all markers are distinct and appear in positive orientation in each genomic map. In this paper, we present several further inapproximability results for MSR-d and its variants CMSR-d, δ-gap-MSR-d, and δ-gap-CMSR-d. One of our main results is that MSR-d is NP-hard to approximate within Ω(d/ log d) even if all markers appear in positive orientation in each genomic map. From the other direction, we show that there is a polynomial-time 2d-approximation algorithm for MSR-d even if d is not a constant but is part of the input.


Maximum Degree Positive Orientation Syntenic Block Minimum Vertex Cover Vertex Marker 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akiyama, J., Chvátal, V.: A short proof of the linear arboricity for cubic graphs. Bull. Liber. Arts & Sci. NMS 2, 1–3 (1981)Google Scholar
  2. 2.
    Akiyama, J., Exoo, G., Harary, F.: Covering and packing in graphs III: cyclic and acyclic invariants. Mathematica Slovaca 30, 405–417 (1980)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Akiyama, J., Exoo, G., Harary, F.: Covering and packing in graphs IV: linear arboricity. Networks 11, 69–72 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoretical Computer Science 237, 123–134 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bar-Yehuda, R., Halldórsson, M.M., Naor, J.(S.), Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36, 1–15 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Berman, P., Karpinski, M.: Improved approximation lower bounds on small occurrence optimization. Electronic Colloquium on Computational Complexity, Report TR03-008 (2003)Google Scholar
  7. 7.
    Bulteau, L., Fertin, G., Jiang, M., Rusu, I.: Tractablity and approximability of maximal strip recovery (submitted)Google Scholar
  8. 8.
    Bulteau, L., Fertin, G., Rusu, I.: Maximal strip recovery problem with gaps: hardness and approximation algorithms. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 710–719. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Chen, Z., Fu, B., Jiang, M., Zhu, B.: On recovering syntenic blocks from comparative maps. Journal of Combinatorial Optimization 18, 307–318 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Chlebík, M., Chlebíková, J.: Complexity of approximating bounded variants of optimization problems. Theoretical Computer Science 354, 320–338 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Dinur, I., Safra, S.: On the hardness of approximating minimum vertex cover. Annals of Mathematics 162, 439–485 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Hazan, E., Safra, S., Schwartz, O.: On the complexity of approximating k-set packing. Computational Complexity 15, 20–39 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Jiang, M.: Inapproximability of maximal strip recovery. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 616–625. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Jiang, M.: Approximation algorithms for predicting RNA secondary structures with arbitrary pseudoknots. IEEE/ACM Transactions on Computational Biology and Bioinformatics 7, 323–332 (2010)CrossRefGoogle Scholar
  15. 15.
    Jiang, M.: On the parameterized complexity of some optimization problems related to multiple-interval graphs. In: Javed, A. (ed.) CPM 2010. LNCS, vol. 6129, pp. 125–137. Springer, Heidelberg (2010)Google Scholar
  16. 16.
    Lyngsø, R.B.: Complexity of pseudoknot prediction in simple models. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 919–931. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43, 425–440 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Trevisan, L.: Non-approximability results for optimization problems on bounded degree instances. In: Proceedings of the 33rd ACM Symposium on Theory of Computing (STOC 2001), pp. 453–461 (2001)Google Scholar
  19. 19.
    Wang, L., Zhu, B.: On the tractability of maximal strip recovery. In: TAMC 2009. LNCS, vol. 5532, pp. 400–409. Springer, Heidelberg (2009)Google Scholar
  20. 20.
    Zheng, C., Zhu, Q., Sankoff, D.: Removing noise and ambiguities from comparative maps in rearrangement analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics 4, 515–522 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Minghui Jiang
    • 1
  1. 1.Department of Computer ScienceUtah State UniversityLoganUSA

Personalised recommendations