## Abstract

Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. This paper presents a new algorithm for the problem of using network supercomputing to perform a large collection of independent tasks, while dealing with undependable processors. The adversary may cause the processors to return bogus results for tasks with certain probabilities, and may cause a subset F of the initial set of processors P to crash. The adversary is constrained in two ways. First, for the set of non-crashed processors P - F , the average probability of a processor returning a bogus result is inferior to 1/2 . Second, the adversary may crash a subset of processors F , provided the size of P - F is bounded from below. We consider two models: the first bounds the size of P - F by a fractional polynomial, the second bounds this size by a poly-logarithm. Both models yield adversaries that are much stronger than previously studied. Our randomized synchronous algorithm is formulated for n processors and t tasks, with n ≤ t, where depending on the number of crashes each live processor is able to terminate dynamically with the knowledge that the problem is solved with high probability. For the adversary constrained by a fractional polynomial, the time complexity of the algorithm is O (t/n ^{ε} log n log log n), its work is O (t log n log log n) and message complexity is O (n log n log log n). For the poly-log constrained adversary, the time complexity is O (n), work is O (t poly log n), and message complexity is O (n poly log n). All bounds are shown to hold with high probability.

Original language | English (US) |
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Title of host publication | Distributed Computing and Networking - 14th International Conference, ICDCN 2013, Proceedings |

Pages | 27-41 |

Number of pages | 15 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

Event | 14th International Conference on Distributed Computing and Networking, ICDCN 2013 - Mumbai, India Duration: Jan 3 2013 → Jan 6 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7730 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference on Distributed Computing and Networking, ICDCN 2013 |
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Country/Territory | India |

City | Mumbai |

Period | 1/3/13 → 1/6/13 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)