TY - JOUR

T1 - Dealing with undependable workers in decentralized network supercomputing

AU - Davtyan, Seda

AU - Konwar, Kishori M.

AU - Russell, Alexander

AU - Shvartsman, Alexander A.

N1 - Funding Information:
This work is supported in part by the NSF Award 1017232 .
Publisher Copyright:
© 2014 Elsevier B.V..

PY - 2015

Y1 - 2015

N2 - 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 12. 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 round complexity of the algorithm is O(tnεlog n log log n), its work is O(tlog n log log n) and message complexity is O(nlognloglogn). For the poly-log constrained adversary, the round complexity is O(t), work is O(tnε), and message complexity is O(n1+ε). All bounds are shown to hold with high probability.

AB - 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 12. 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 round complexity of the algorithm is O(tnεlog n log log n), its work is O(tlog n log log n) and message complexity is O(nlognloglogn). For the poly-log constrained adversary, the round complexity is O(t), work is O(tnε), and message complexity is O(n1+ε). All bounds are shown to hold with high probability.

KW - Distributed algorithms

KW - Fault-tolerance

KW - Internet supercomputing

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U2 - 10.1016/j.tcs.2014.10.015

DO - 10.1016/j.tcs.2014.10.015

M3 - Article

AN - SCOPUS:84927913885

SN - 0304-3975

VL - 561

SP - 96

EP - 112

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - PB

ER -