Local management of a global resource in a communication network
Journal of the ACM (JACM)
Cache oblivious search trees via binary trees of small height
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Lower Bounds for Monotonic List Labeling
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
A Sparse Table Implementation of Priority Queues
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A locality-preserving cache-oblivious dynamic dictionary
Journal of Algorithms
A Tight Lower Bound for Online Monotonic List Labeling
SIAM Journal on Discrete Mathematics
SIAM Journal on Computing
Information Processing Letters
Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
On online labeling with polynomially many labels
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On randomized online labeling with polynomially many labels
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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 rm 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 In the case that m = Cn for some C1, algorithms for this problem with cost O(log(n)2) per item have been given [Itai et al. (1981), Willard (1992), Bender et al. (2002)]. When m=n, algorithms with cost O(log(n)3) per item were given [Zhang (1993),Bird and Sadnicki (2007)]. 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 Ω(log(n)2) for the restricted class of smooth algorithms [Dietz et al. (2005), Zhang (1993)]. 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.