Optimal resilient dynamic dictionaries

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Optimal resilient dynamic dictionaries (2007)

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by Gerth Stølting Brodal , Rolf Fagerberg , Irene Finocchi , Fabrizio Grandoni, Giuseppe F. Italiano , Allan Grønlund Jørgensen , Gabriel Moruz , Thomas Mølhave

Venue:	IN PROCEEDINGS OF 15TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
Citations:	12 - 8 self

BibTeX

@INPROCEEDINGS{Brodal07optimalresilient,
    author = {Gerth Stølting Brodal and Rolf Fagerberg and Irene Finocchi and Fabrizio Grandoni and Giuseppe F. Italiano and Allan Grønlund Jørgensen and Gabriel Moruz and Thomas Mølhave},
    title = {Optimal resilient dynamic dictionaries},
    booktitle = {IN PROCEEDINGS OF 15TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA},
    year = {2007},
    pages = {347--358},
    publisher = {}
}

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Abstract

We investigate the problem of computing in the presence of faults that may arbitrarily (i.e., adversarially) corrupt memory locations. In the faulty memory model, any memory cell can get corrupted at any time, and corrupted cells cannot be distinguished from uncorrupted ones. An upper bound δ on the number of corruptions and O(1) reliable memory cells are provided. In this model, we focus on the design of resilient dictionaries, i.e., dictionaries which are able to operate correctly (at least) on the set of uncorrupted keys. We first present a simple resilient dynamic search tree, based on random sampling, with O(log n+δ) expected amortized cost per operation, and O(n) space complexity. We then propose an optimal deterministic static dictionary supporting searches in Θ(log n+δ) time in the worst case, and we show how to use it in a dynamic setting in order to support updates in O(log n + δ) amortized time. Our dynamic dictionary also supports range queries in O(log n+δ+t) worst case time, where t is the size of the output. Finally, we show that every resilient search tree (with some reasonable properties) must take Ω(log n + δ) worst-case time per search.

Keyphrases

optimal resilient dynamic dictionary reliable memory cell worst-case time random sampling memory cell reasonable property space complexity resilient search tree simple resilient dynamic search tree optimal deterministic static dictionary corrupt memory location dynamic dictionary dynamic setting amortized cost uncorrupted key uncorrupted one faulty memory model range query resilient dictionary case time upper bound

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