Abstract
We give a randomized algorithm for sorting strings in external memory. For K binary strings comprising N words in total, our algorithm finds the sorted order and the longest common prefix sequence of the strings using \(O(\frac{K}{B}log_{M/B}(\frac{K}{M})log(\frac{N}{K}) + \frac{N}{B})\) I/Os. This bound is never worse than \(O(\frac{K}{B}log_{M/B}(\frac{K}{M})log log_{M/B}(\frac{K}{M}) + \frac{N}{B})\) I/Os, and improves on the (deterministic) algorithm of Arge et al. (On sorting strings in external memory, STOC ’97). The error probability of the algorithm can be chosen as O(N \(^{\rm -{\it c}}\)) for any positive constant c. The algorithm even works in the cache-oblivious model under the tall cache assumption, i.e,, assuming M > B 1 + ε for some ε > 0. An implication of our result is improved construction algorithms for external memory string dictionaries.
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References
Aggarwal, A., Vitter, J.S.: The Input/Output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1127 (1988)
Andersson, A., Hagerup, T., Nilsson, S., Raman, R.: Sorting in linear time? J. Comput. System Sci. 57(1), 74–93 (1998)
Andersson, A., Nilsson, S.: A new efficient radix sort. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), pp. 714–721. IEEE Comput. Soc. Press, Los Alamitos (1994)
Arge, L.: External memory data structures. In: Abello, J., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Massive Data Sets, pp. 313–358. Kluwer Academic Publishers, Dordrecht (2002)
Arge, L., Bender, M.A., Demaine, E.D., Holland-Minkley, B., Munro, J.I.: Cache-oblivious priority queue and graph algorithm applications. In: ACM. (ed.) Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 268–276. ACM Press, New York (2002)
Arge, L., Brodal, G.S., Fagerberg, R.: Cache-oblivious data structures. In: Mehta, D., Sahni, S. (eds.) Handbook on Data Structures and Applications, CRC Press, Boca Raton (2005)
Arge, L., Ferragina, P., Grossi, R., Vitter, J.S.: On sorting strings in external memory (extended abstract). In: ACM (ed.) Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC 1997), pp. 540–548. ACM Press, New York (1997)
Bentley, J., Sedgewick, R.: Fast algorithms for sorting and searching strings. In: Proc. 8th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 360–369 (1997)
Brodal, G.S.: Cache-oblivious algorithms and data structures. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 3–13. Springer, Heidelberg (2004)
Brodal, G.S., Fagerberg, R.: Cache oblivious distribution sweeping. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 426–438. Springer, Heidelberg (2002)
Brodal, G.S., Fagerberg, R.: On the limits of cache-obliviousness. In: Proc. 35th Annual ACM Symposium on Theory of Computing, pp. 307–315 (2003)
Brodal, G.S., Fagerberg, R.: Cache-oblivious string dictionaries. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006) (to appear, 2006)
Demaine, E.D.: Cache-oblivious data structures and algorithms. In: Proc. EFF summer school on massive data sets. LNCS, Springer, Heidelberg (to appear)
Farach-Colton, M., Ferragina, P., Muthukrishnan, S.: On the sorting-complexity of suffix tree construction. J. ACM 47(6), 987–1011 (2000)
Ferragina, P., Grossi, R.: The string B-tree: a new data structure for string search in external memory and its applications. J. ACM 46(2), 236–280 (1999)
Fredman, M.L., Willard, D.E.: Trans-dichotomous algorithms for minimum spanning trees and shortest paths. J. Comput. System Sci. 48(3), 533–551 (1994)
Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache oblivious algorithms. In: 40th Annual IEEE Symposium on Foundations of Computer Science, pp. 285–298. IEEE Computer Society Press, Los Alamitos (1999)
Han, Y., Thorup, M.: Integer sorting in \(O(n\sqrt{\log\log n})\) expected time and linear space. In: Proceedings of the 43rd Annual Symposium on Foundations of Computer Science (FOCS 2002), pp. 135–144 (2002)
Kärkkäinen, J., Sanders, P.: Simple linear work suffix array construction. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 943–955. Springer, Heidelberg (2003)
Karp, R.M., Miller, R.E., Rosenberg, A.L.: Rapid identification of repeated patterns in strings, trees and arrays. In: Proceedings of the 4th Annual ACM Symposium on Theory of Computing (STOC 2072), pp. 125–136 (1972)
Meyer, U., Sanders, P., Sibeyn, J.F. (eds.): Algorithms for Memory Hierarchies. LNCS, vol. 2625. Springer, Berlin (2003)
Morrison, D.R.: PATRICIA - practical algorithm to retrieve information coded in alphanumeric. J. ACM 15(4), 514–534 (1968)
Vitter, J.S.: External memory algorithms and data structures: Dealing with MASSIVE data. ACM Computing Surveys 33(2), 209–271 (2001)
Vitter, J.S.: Geometric and spatial data structures in external memory. In: Mehta, D., Sahni, S. (eds.) Handbook on Data Structures and Applications, CRC Press, Boca Raton (2005)
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Fagerberg, R., Pagh, A., Pagh, R. (2006). External String Sorting: Faster and Cache-Oblivious. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_4
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DOI: https://doi.org/10.1007/11672142_4
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