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Tight lower bounds for the online labeling problem
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SYSNO ASEP 0386313 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Tight lower bounds for the online labeling problem Author(s) Bulánek, Jan (MU-W) RID, SAI
Koucký, Michal (MU-W) RID, SAI, ORCID
Saks, M. (US)Source Title Proceedings of the 44th Symposium on Theory of Computing, STOC'2012. - New York : ACM, 2012 / Karloff H.J. ; Pitassi T. - ISBN 978-1-4503-1245-5 Pages s. 1185-1198 Number of pages 14 s. Publication form Print - P Action STOC'12 Symposium on Theory of Computing Conference /44./ Event date 19.05.2012-22.05.2012 VEvent location New York Country US - United States Event type WRD Language eng - English Country US - United States Keywords online labeling ; file maintenance problem ; lower bounds Subject RIV BA - General Mathematics R&D Projects GAP202/10/0854 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 EID SCOPUS 84862611470 DOI 10.1145/2213977.2214083 Annotation We consider the file maintenance problem (also called the online labeling problem) in which n integer items from the set {1,...,r} are to be stored in an array of size m >= n. The items are presented sequentially in an arbitrary order, and must be stored in the array in sorted order (but not necessarily in consecutive locations in the array). Each new item must be stored in the array before the next item is received. If r < m then we can simply store item j in location j but if r > m then we may have to shift the location of stored items to make space for a newly arrived item. The algorithm is charged each time an item is stored in the array, or moved to a new location. The goal is to minimize the total number of such moves the algorithm has to do. In this paper we prove lower bounds Omega(log^2 n), for m=Cn, C>1, and Omega(log^3 n), for m=n, that show that known algorithms for this problem are optimal, up to constant factors. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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