Abstract
The best known approximation ratio for the shortest superstring problem is \(2\frac{11}{23}\) (Mucha, 2012). In this note, we improve this bound for the case when the length of all input strings is equal to r, for r ≤ 7. E.g., for strings of length 3 we get a \(1\frac{1}{3}\)-approximation. An advantage of the algorithm is that it is extremely simple both to implement and to analyze. Another advantage is that it is based on de Bruijn graphs. Such graphs are widely used in genome assembly (one of the most important practical applications of the shortest common superstring problem). At the same time these graphs have only a few applications in theoretical investigations of the shortest superstring problem.
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References
Armen, C., Stein, C.: A \(2\frac{3}{4}\)-Approximation Algorithm for the Shortest Superstring Problem. Tech. rep., Dartmouth College, Hanover, NH, USA (1994)
Armen, C., Stein, C.: Improved length bounds for the shortest superstring problem. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 494–505. Springer, Heidelberg (1995)
Armen, C., Stein, C.: A \(2\frac{2}{3}\)-Approximation for the Shortest Superstring Problem. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 87–101. Springer, Heidelberg (1996)
Blum, A., Jiang, T., Li, M., Tromp, J., Yannakakis, M.: Linear approximation of shortest superstrings. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, STOC 1991, pp. 328–336. ACM, New York (1991)
Breslauer, D., Jiang, T., Jiang, Z.: Rotations of periodic strings and short superstrings. J. Algorithms 24(2), 340–353 (1997)
Christofides, N., Campos, V., Corberan, A., Mota, E.: An algorithm for the Rural Postman problem on a directed graph. In: Netflow at Pisa, Mathematical Programming Studies, vol. 26, pp. 155–166. Springer, Heidelberg (1986)
Crochemore, M., Cygan, M., Iliopoulos, C., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T.: Algorithms for three versions of the shortest common superstring problem. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 299–309. Springer, Heidelberg (2010)
Czumaj, A., Gasieniec, L., Piotrow, M., Rytter, W.: Parallel and sequential approximation of shortest superstrings. In: Schmidt, E.M., Skyum, S. (eds.) SWAT 1994. LNCS, vol. 824, pp. 95–106. Springer, Heidelberg (1994)
Eiselt, H.A., Gendreau, M., Laporte, G.: Arc Routing Problems, Part II: The Rural Postman Problem. Operations Research 43(3), 399–414 (1995)
Gallant, J., Maier, D., Storer, J.A.: On finding minimal length superstrings. Journal of Computer and System Sciences 20(1), 50–58 (1980)
Groves, G., van Vuuren, J.: Efficient heuristics for the Rural Postman Problem. ORiON 21(1), 33–51 (2005)
Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs. J. ACM 52, 602–626 (2005)
Kaplan, H., Shafrir, N.: The greedy algorithm for shortest superstrings. Inf. Process. Lett. 93(1), 13–17 (2005)
Karpinski, M., Schmied, R.: Improved Lower Bounds for the Shortest Superstring and Related Problems. CoRR abs/1111.5442v3 (2012)
Kosaraju, S.R., Park, J.K., Stein, C.: Long tours and short superstrings. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, SFCS 1994, pp. 166–177. IEEE Computer Society, Washington, DC (1994)
Mucha, M.: Lyndon Words and Short Superstrings. In: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013. Society for Industrial and Applied Mathematics (2013)
Ott, S.: Lower bounds for approximating shortest superstrings over an alphabet of size 2. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, p. 55. Springer, Heidelberg (1999)
Paluch, K., Elbassioni, K., van Zuylen, A.: Simpler Approximation of the Maximum Asymmetric Traveling Salesman Problem. In: STACS 2012. LIPIcs, vol. 14, pp. 501–506 (2012)
Pevzner, P.A., Tang, H., Waterman, M.S.: An Eulerian path approach to DNA fragment assembly. Proc. Natl. Acad. Sci. 98(17), 9748–9753 (2001)
Sahni, S., Gonzalez, T.: P-Complete Approximation Problems. J. ACM 23, 555–565 (1976)
Sweedyk, Z.: \(2\frac{1}{2}\)-Approximation Algorithm for Shortest Superstring. SIAM J. Comput. 29(3), 954–986 (1999)
Tarhio, J., Ukkonen, E.: A greedy approximation algorithm for constructing shortest common superstrings. Theoretical Computer Science 57(1), 131–145 (1988)
Teng, S.H., Yao, F.: Approximating shortest superstrings. In: Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science, SFCS 1993, pp. 158–165. IEEE Computer Society, Washington, DC (1993)
Turner, J.S.: Approximation algorithms for the shortest common superstring problem. Information and Computation 83(1), 1–20 (1989)
Vassilevska, V.: Explicit Inapproximability Bounds for the Shortest Superstring Problem. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 793–800. Springer, Heidelberg (2005)
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Golovnev, A., Kulikov, A.S., Mihajlin, I. (2013). Approximating Shortest Superstring Problem Using de Bruijn Graphs. In: Fischer, J., Sanders, P. (eds) Combinatorial Pattern Matching. CPM 2013. Lecture Notes in Computer Science, vol 7922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38905-4_13
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DOI: https://doi.org/10.1007/978-3-642-38905-4_13
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