Abstract
We study three closely related problems motivated by the prediction of RNA secondary structures with arbitrary pseudoknots: the Maximum Base Pair Stackings problem proposed by Ieong et al. [19] , the Maximum Stacking Base Pairs problem proposed by Lyngsø [22], and the 2-Interval Pattern problem proposed by Vialette [36] . For Maximum Base Pair Stackings and Maximum Stacking Base Pairs, we present improved approximation algorithms that can incorporate covariance information from comparative analysis as explicit input of candidate base pairs. For 2-Interval Pattern, we present improved approximation algorithms on unitary and near-unitary input, and propose a new variant called Length-Weighted Balanced 2-Interval Pattern, which is natural in the nearest-neighbor energy model that emphasizes base pair stacking.
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Abrahams, J.P., van den Berg, M., van Batenburg, E., Pleij, C.: Prediction of RNA secondary structure, including pseudoknotting, by computer simulation. Nucleic Acids Research 18(10), 3035–3044 (1990)
Akutsu, T.: Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discrete Applied Mathematics 104(1-3), 45–62 (2000)
Bafna, V., Narayanan, B., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Applied Mathematics 71, 41–53 (1996)
Bar-Yehuda, R., Halldórsson, M.M., Naor, J(S.), Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36(1), 1–15 (2006)
van Batenburg, F.H.D., Gultyaev, A.P., Pleij, C.W.A.: An APL-programmed genetic algorithm for the prediction of RNA secondary structure. Journal of Theoretical Biology 174(3), 269–280 (1995)
van Batenburg, F.H.D., Gultyaev, A.P., Pleij, C.W.A., Ng, J., Oliehoek, J.: Pseudobase: a database with RNA pseudoknots. Nucleic Acids Research 28(1), 201–204 (2000)
Berman, P.: A d/2 approximation for maximum weight independent set in d-claw free graphs. Nordic Journal of Computing 7, 178–184 (2000)
Berman, P., DasGupta, B., Muthukrishnan, S.: Simple approximation algorithm for nonoverlapping local alignments. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’02), pp. 677–678 (2002)
Blin, G., Fertin, G., Vialette, S.: New results for the 2-interval pattern problem. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 311–322. Springer, Heidelberg (2004)
Cary, R.B., Stormo, G.D.: Graph-theoretic approach to RNA modeling using comparative data. In: Proceedings of the 3rd International Conference on Intelligent Systems for Molecular Biology (ISMB’95), pp. 75–80 (1995)
Chen, E., Yang, L., Yuan, H.: Improved algorithms for largest cardinality 2-interval pattern problem. Journal of Combinatorial Optimization, Special Issue on Bioinformatics (to appear)
Crochemore, M., Hermelin, D., Landau, G.M., Vialette, S.: Approximating the 2-interval pattern problem. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 426–437. Springer, Heidelberg (2005)
Crochemore, M., Hermelin, D., Landau, G.M., Rawitz, D., Vialette, S.: Approximating the 2-interval pattern problem. Theoretical Computer Science (to appear)
Gultyaev, A.P., van Batenburg, F.H.D., Pleij, C.W.A.: The computer simulation of RNA folding pathways using a genetic algorithm. Journal of Molecular Biology 250(1), 37–51 (1995)
Halldórsson, M.M.: Approximating discrete collections via local improvements. In: Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’95), pp. 160–169 (1995)
Hofacker, I.L.: Vienna RNA secondary structure server. Nucleic Acids Research 31(13), 3429–3431 (2003)
Hofacker, I.L., Fontana, W., Stadler, P.F., Bonhoeffer, S., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatshefte für Chemie 125(2), 167–188 (1994)
Hurkens, C.A.J., Schrijver, A.: On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM Journal on Discrete Mathematics 2(1), 68–72 (1989)
Ieong, S., Kao, M.-Y., Lam, T.-W., Sung, W.-K., Yiu, S.-M.: Predicting RNA secondary structure with arbitrary pseudoknots by maximizing the number of stacking pairs. Journal of Computational Biology 10(6), 981–995 (2003)
Jiang, M.: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. Journal of Combinatorial Optimization, Special Issue on Bioinformatics (to appear)
Jiang, M.-h., Mayne, M., Gillespie, J.: Delta: A toolset for the structural analysis of biological sequences on a 3D triangular lattice. In: Măndoiu, I.I., Zelikovsky, A. (eds.) ISBRA 2007. LNCS (LNBI), vol. 4463, pp. 518–529. Springer, Heidelberg (2007)
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)
Lyngsø, R.B., Pedersen, C.N.S.: RNA pseudoknot prediction in energy-based models. Journal of Computational Biology 7(3/4), 409–427 (2000)
Lyngsø, R.B., Zuker, M., Pedersen, C.N.S.: Fast evaluation of interval loops in RNA secondary structure prediction. Bioinformatics 15(6), 440–445 (1999)
Mathews, D.H., Sabina, J., Zuker, M., Turner, D.H.: Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology 288(5), 911–940 (1999)
Micali, S., Vazirani, V.V.: 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 (1980)
Nussinov, R., Pieczenik, G., Griggs, J.R., Kleitman, D.J.: Algorithms for loop matching. SIAM Journal on Applied Mathematics 35(1), 68–82 (1978)
Pace, N.R., Thomas, B.C., Woese, C.R.: Probing RNA structure, function, and history by comparative analysis. In: The RNA World, 2nd edn., pp. 113–141. Cold Spring Harbor Laboratory Press, Cold Spring Harbor (1999)
Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. Journal of Molecular Biology 285, 2053–2068 (1999)
Ruan, J., Stormo, G.D., Zhang, W.: An iterated loop matching approach to the prediction of RNA secondary structure with pseudoknots. Bioinformatics 20(1), 58–66 (2004)
Sankoff, D.: Simultaneous solution of the RNA folding, alignment and protosequence problems. SIAM Journal on Applied Mathematics 45(5), 810–825 (1985)
Shapiro, B.A., Wu, J.C.: Predicting RNA H-type pseudoknots with the massively parallel genetic algorithm. Computer Applications in the Biosciences 13(4), 459–471 (1997)
Tabaska, J.E., Cary, R.B., Gabow, H.N., Stormo, G.D.: An RNA folding method capable of identifying pseudoknots and base triples. Bioinformatics 14(8), 691–699 (1998)
Tinoco, I., Borer, P.N., Dengler, B., Levine, M.D., Uhlenbeck, O.C., Crothers, D.M., Gralla, J.: Improved estimation of secondary structure in ribonucleic acids. Nature New Biology 246, 40–42 (1973)
Uemura, Y., Hasegawa, A., Kobayashi, S., Yokomori, T.: Tree adjoining grammars for RNA structure prediction. Theoretical Computer Science 210(2), 277–303 (1999)
Vialette, S.: On the computational complexity of 2-interval pattern matching problems. Theoretical Computer Science 312, 223–249 (2004)
Zuker, M.: Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Research 31(13), 3406–3415 (2003)
Zuker, M., Sankoff, D.: RNA secondary structures and their prediction. Bulletin of Mathematical Biology 46, 591–621 (1984)
Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Research 9(1), 133–148 (1981)
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Jiang, M. (2007). Improved Approximation Algorithms for Predicting RNA Secondary Structures with Arbitrary Pseudoknots. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_38
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DOI: https://doi.org/10.1007/978-3-540-72870-2_38
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