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# Tight lower bounds for the online labeling problem

1. 1.
0386313 - MÚ 2013 RIV US eng C - Conference Paper (international conference)
Bulánek, Jan - Koucký, Michal - Saks, M.
Tight lower bounds for the online labeling problem.
Proceedings of the 44th Symposium on Theory of Computing, STOC'2012. New York: ACM, 2012 - (Karloff, H.; Pitassi, T.), s. 1185-1198. ISBN 978-1-4503-1245-5.
[STOC'12 Symposium on Theory of Computing Conference /44./. New York (US), 19.05.2012-22.05.2012]
R&D Projects: GA ČR GAP202/10/0854
Institutional support: RVO:67985840
Keywords : online labeling * file maintenance problem * lower bounds
Subject RIV: BA - General Mathematics
http://dl.acm.org/citation.cfm?id=2213977.2214083&coll=DL&dl=GUIDE&CFID=245194486&CFTOKEN=14126751

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.