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Sorting and Searching in Faulty Memories

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Abstract

In this paper we investigate the design and analysis of algorithms resilient to memory faults. We focus on algorithms that, despite the corruption of some memory values during their execution, are nevertheless able to produce a correct output at least on the set of uncorrupted values. In this framework, we consider two fundamental problems: sorting and searching. In particular, we prove that any O(nlog n) comparison-based sorting algorithm can tolerate the corruption of at most O((nlog n)1/2) keys. Furthermore, we present one comparison-based sorting algorithm with optimal space and running time that is resilient to O((nlog n)1/3) memory faults. We also prove polylogarithmic lower and upper bounds on resilient searching.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, Via Salaria 113, 00198, Rome, Italy

    Irene Finocchi

  2. Dipartimento di Informatica, Sistemi e Produzione, Università degli Studi di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

Authors
  1. Irene Finocchi
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  2. Giuseppe F. Italiano
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Correspondence to Irene Finocchi.

Additional information

This work has been partially supported by the Sixth Framework Programme of the EU under Contract Number 507613 (Network of Excellence “EuroNGI: Designing and Engineering of the Next Generation Internet”) and by MIUR, the Italian Ministry of Education, University and Research, under Project ALGO-NEXT (“Algorithms for the Next Generation Internet and Web: Methodologies, Design and Experiments”). A preliminary version of this work was presented at the 36th ACM Symposium on Theory of Computing (STOC’04) .

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Finocchi, I., Italiano, G.F. Sorting and Searching in Faulty Memories. Algorithmica 52, 309–332 (2008). https://doi.org/10.1007/s00453-007-9088-4

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