Abstract
We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets. Given the expression and the sizes of the sets, we are interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume no set is repeated in the expression. We show a lower bound on this problem and present an algorithm that matches the lower bound asymptotically.
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References
Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. In: Proceedings of the seventh international conference on World Wide Web, vol. 7, pp. 107–117. Elsevier Science Publishers B. V, Amsterdam (1998)
Brown, M.R., Tarjan, R.E.: A fast merging algorithm. J. ACM 26(2), 211–226 (1979)
Brown, M.R., Tarjan, R.E.: Design and analysis of a data structure for representing sorted lists. SIAM Journal of Computing 9(3), 594–614 (1980)
Demaine, E.D., Lopez-Ortiz, A., Munro, J.I.: Adaptive set intersections, unions, and differences. In: Proc. of Eleventh ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 743–752 (2000)
Hwang, F.K., Lin, S.: A simple algorithm for merging two disjoint linearly ordered sets. SIAM Journal on Computing 1(1), 31–39 (1972)
Lee, G., Park, M., Won, H.: Using syntactic information in handling natural language quries for extended boolean retrieval model. In: Proceedings of the 4th international workshop on information retrieval with Asian languages (1999)
Mauldin, M.I.Lycos Inc., and PA Pittsburgh. Lycos: design choices in an internet search service. IEEE Expert, 12(1):8–11, 1997.
Mirzazadeh, M.: Adaptive comparison-based algorithms for evaluating set queries. Master’s thesis, School of Computer Science, University of Waterloo (2004)
Pugh, W.: A skip list cookbook. Technical Report CS-TR-2286.1, University of Maryland (1990)
Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill, Inc., New York (1990)
Witten, I.H., Bell, T.C., Moffat, A.: Managing Gigabytes: Compressing and Indexing Documents and Images. John Wiley & Sons, Inc., Chichester (1994)
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Chiniforooshan, E., Farzan, A., Mirzazadeh, M. (2005). Worst Case Optimal Union-Intersection Expression Evaluation. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_15
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DOI: https://doi.org/10.1007/11523468_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
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