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- W2471701653 abstract "We consider the le maintenance problem (also called the online labeling problem) in which n integer items from the setf1;:::;rg 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. This problem is non-trivial when n m 1, algorithms for this problem with costO(log(n) 2 ) per item have been given [IKR81, Wil92, BCD + 02]. When m = n, algorithms with cost O(log(n) 3 ) per item were given [Zha93, BS07]. In this paper we prove lower bounds that show that these algorithms are optimal, up to constant factors. Previously, the only lower bound known for this range of parameters was a lower bound of (log( n) 2 ) for the restricted class of smooth algorithms [DSZ05a, Zha93]. We also provide an algorithm for the sparse case: If the number of items is polylogarithmic in the array size then the problem can be solved in amortized constant time per item." @default.
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- W2471701653 date "2011-12-23" @default.
- W2471701653 modified "2023-09-23" @default.
- W2471701653 title "Tight lower bounds for online labeling problem" @default.
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