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Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property

Authors Gerth Stølting Brodal, Casper Kejlberg-Rasmussen



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Gerth Stølting Brodal
Casper Kejlberg-Rasmussen

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Gerth Stølting Brodal and Casper Kejlberg-Rasmussen. Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 112-123, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.112

Abstract

In this paper we present an implicit dynamic dictionary with the working-set property, supporting insert(e) and delete(e) in O(log n) time, predecessor(e) in O(log l_{p(e)}) time, successor(e) in O(log l_{s(e)}) time and search(e) in O(log min(l_{p(e)},l_{e}, l_{s(e)})) time, where n is the number of elements stored in the dictionary, l_{e} is the number of distinct elements searched for since element e was last searched for and p(e) and s(e) are the predecessor and successor of e, respectively. The time-bounds are all worst-case. The dictionary stores the elements in an array of size n using *no* additional space. In the cache-oblivious model the log is base B and the cache-obliviousness is due to our black box use of an existing cache-oblivious implicit dictionary. This is the first implicit dictionary supporting predecessor and successor searches in the working-set bound. Previous implicit structures required O(log n) time.
Keywords
  • working-set property
  • dictionary
  • implicit
  • cache-oblivious
  • worst-case
  • external memory
  • I/O efficient

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