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A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem

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Abstract

The 2-interval pattern problem over its various models and restrictions was proposed by Vialette (2004) for the application of RNA secondary structure prediction. We present an O(n 3logn)-time 2-approximation algorithm for the problem of finding a largest { < ,\(\{<,\between\}\)-structured subset of 2-intervals given an input 2-interval set of size n. This greatly improves the previous best approximation ratio of 6 by Crochemore et al. (2005).

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References

  • Bar-Yehuda R, Halldórsson MM, J(S), Naor J, Shachnai H, Shapira I (2002) Scheduling split intervals. In: Proceedings of the 13th annual ACM-SIAM symposium on discrete algorithms (SODA’02), pp 732–741

  • Blin G, Fertin G, Vialette S (2004) New results for the 2-interval pattern problem. In: Proceedings of the 15th annual symposium on combinatorial pattern matching (CPM’04), LNCS 3109, pp 311–322

  • Crochemore M, Hermelin D, Landau GM, Vialette S (2005) Approximating the 2-interval pattern problem. In: Proceedings of the 13th annual European symposium on algorithms (ESA’05), LNCS 3669, pp 426–437

  • Felsner S, Müller R, Wernisch L (1997) Trapezoid graphs and generalizations, geometry and algorithms. Disc Appl Math, 74:13–32

    Article  MATH  Google Scholar 

  • Micali S, Vazirrani VV (1980) An \(O(\sqrt{|V|} |E|)\) algorithm for finding maximum matching in general graphs. In: Proceedings of the 21st annual symposium on foundations of computer science (FOCS’80), pp 17–27

  • Vialette S (2004) On the computational complexity of 2-interval pattern matching problems. Theor Comp Sci 312:223–249

    Article  MATH  MathSciNet  Google Scholar 

  • Yuan H, Yang L, Chen E (2005) Improved algorithms for largest cardinality 2-interval pattern problem. In: Proceedings of the 16th international symposium on algorithms and computation (ISAAC’05), LNCS 3827, pp. 412–421

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Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, Utah, 84322-4205, USA

    Minghui Jiang

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  1. Minghui Jiang
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Correspondence to Minghui Jiang.

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Jiang, M. A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. J Comb Optim 13, 217–221 (2007). https://doi.org/10.1007/s10878-006-9024-6

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  • DOI: https://doi.org/10.1007/s10878-006-9024-6

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