Abstract
This paper introduces a simple intersection algorithm for two sorted sequences that is fast on average. It is related to the multiple searching problem and to merging. We present the worst and average case analysis, showing that in the former, the complexity nicely adapts to the smallest list size. In the later case, it performs less comparisons than the total number of elements on both inputs when n = αm (α > 1). Finally, we show its application to fast query processing in Web search engines, where large intersections, or differences, must be performed fast.
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References
Baeza-Yates, R.A.: Efficient Text Searching. PhD thesis, Dept. of Computer Science, University of Waterloo, Also as Research Report CS-89-17 (May 1989)
Baeza-Yates, R., Bradford, P.G., Culberson, J.C., Rawlins, G.J.E.: The Complexity of Multiple Searching (1993)(unpublished manuscript)
Baeza-Yates, R., Ribeiro-Neto, B.: Modern Information Retrieval, p. 513. ACM Press/Addison-Wesley (1999)
Baeza-Yates, R., Saint-Jean, F.: A Three Level Search Engine Index based in Query Log Distribution. In: Nascimento, M.A., de Moura, E.S., Oliveira, A.L. (eds.) SPIRE 2003. LNCS, vol. 2857, pp. 56–65. Springer, Heidelberg (2003)
Baeza-Yates, R.: Query Usage Mining in Search Engines. In: Scime, A. (ed.) Web Mining: Applications and Techniques, Idea Group (2004)
Barbay, J., Kenyon, C.: Adaptive Intersection and t-Threshold Problems. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, January 2002, pp. 390–399 (2002)
Brin, S., Page, L.: The anatomy of a large-scale hypertextualWeb search engine. In: 7th WWW Conference, Brisbane, Australia (April 1998)
Demaine, E.D., López-Ortiz, A., Munro, J.I.: Adaptive set intersections, unions, and differences. In: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, January 2000, pp. 743–752 (2000)
Demaine, E.D., López-Ortiz, A., Munro, J.I.: Experiments on Adaptive set intersections for text retrieval systems. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, Springer, Heidelberg (2002)
Paul, D., Kurt, M., Rajeev, R., Christian, U.: Lower Bounds for Set Intersection Queries. In: Proceedings of the 4th Annual Symposium on Discrete Algorithms, pp. 194–201 (1993)
David, D., Richard, L.: On the Complexity of Computations Under Varying Sets of Primitives. Journal of Computer and Systems Sciences 18, 86–91 (1979)
de la Vega, W.F., Kannan, S., Santha, M.: Two probabilistic results on merging. SIAM J. on Computing 22(2), 261–271 (1993)
de la Vega, W.F., Frieze, A.M., Santha, M.: Average case analysis of the merging algorithm of Hwang and Lin. Algorithmica 22(4), 483–489 (1998)
Hwang, F.K., Lin, S.: A Simple algorithm for merging two disjoint linearly ordered lists. SIAM J. on Computing 1, 31–39 (1972)
Rawlins, Gregory, J.E.: Compared to What?: An Introduction the the Analysis of Algorithms. Computer Science Press/W. H. Freeman (1992)
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Baeza-Yates, R. (2004). A Fast Set Intersection Algorithm for Sorted Sequences. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_30
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DOI: https://doi.org/10.1007/978-3-540-27801-6_30
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