Local management of a global resource in a communication network
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
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
Tight lower bounds for the online labeling problem
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On online labeling with polynomially many labels
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We prove an optimal lower bound on the complexity of randomized algorithms for the online labeling problem with polynomially many labels. All previous work on this problem (both upper and lower bounds) only applied to deterministic algorithms, so this is the first paper addressing the (im)possibility of faster randomized algorithms. Our lower bound Ω(n log(n)) matches the complexity of a known deterministic algorithm for this setting of parameters so it is asymptotically optimal. In the online labeling problem with parameters n and m we are presented with a sequence of nitems from a totally ordered universe U and must assign each arriving item a label from the label set {1,2,…,m} so that the order of labels (strictly) respects the ordering on U. As new items arrive it may be necessary to change the labels of some items; such changes may be done at any time at unit cost for each change. The goal is to minimize the total cost. An alternative formulation of this problem is the file maintenance problem, in which the items, instead of being labeled, are maintained in sorted order in an array of length m, and we pay unit cost for moving an item.