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Minimum Congestion Redundant Assignments to Tolerate Random Faults

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We consider the problem of computing minimum congestion, fault-tolerant, redundant assignments of messages to faulty, parallel delivery channels. In particular, we are given a set Kof faulty channels, each having an integer capacity c i and failing independently with probability f i . We are also given a set Mof messages to be delivered over K , and a fault-tolerance constraint (1-ɛ) , and we seek a redundant assignment ϕthat minimizes congestion \lilsf Cong(ϕ) , i.e. the maximum channel load, subject to the constraint that, with probability no less than (1-ɛ) , all the messages have a copy on at least one active channel. We present a polynomial-time 4-approximation algorithm for identical capacity channels and arbitrary message sizes, and a 2 \lceil\ln(|K|/\e)/\ln(1/fmax ) \rceil -approximation algorithm for related capacity channels and unit size messages.

Both algorithms are based on computing a collection {K 1 , \ldots, K ν }of disjoint channel subsets such that, with probability no less than (1-ɛ) , at least one channel is active in each subset. The objective is to maximize the sum of the minimum subset capacities. Since the exact version of this problem is NP -complete, we provide a 2-approximation algorithm for identical capacities, and a polynomial-time (8+ \rm o (1)) -approximation algorithm for arbitrary capacities.

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Fotakis, Spirakis Minimum Congestion Redundant Assignments to Tolerate Random Faults . Algorithmica 32, 396–422 (2002).

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