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Tolerant Algorithms

  • Rolf Klein
  • Rainer Penninger
  • Christian Sohler
  • David P. Woodruff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

Assume we are interested in solving a computational task, e.g., sorting n numbers, and we only have access to an unreliable primitive operation, for example, comparison between two numbers. Suppose that each primitive operation fails with probability at most p and that repeating it is not helpful, as it will result in the same outcome. Can we still approximately solve our task with probability 1 − f(p) for a function f that goes to 0 as p goes to 0? While previous work studied sorting in this model, we believe this model is also relevant for other problems. We
  • find the maximum of n numbers in O(n) time,

  • solve 2D linear programming in O(n logn) time,

  • approximately sort n numbers in O(n 2) time such that each number’s position deviates from its true rank by at most O(logn) positions,

  • find an element in a sorted array in O(logn loglogn) time.

Our sorting result can be seen as an alternative to a previous result of Braverman and Mossel (SODA, 2008) who employed the same model. While we do not construct the maximum likelihood permutation, we achieve similar accuracy with a substantially faster running time.

Keywords

Intersection Point Error Probability Full Version Primitive Operation True Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rolf Klein
    • 1
  • Rainer Penninger
    • 1
  • Christian Sohler
    • 2
  • David P. Woodruff
    • 3
  1. 1.University of BonnGermany
  2. 2.TU DortmundGermany
  3. 3.IBM Research-AlmadenUSA

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