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Internet supercomputing is an approach to solving partitionable,computation-intensive problems by harnessing the power of a vast number ofinterconnected computers. This paper presents a new algorithm for the problemof using network supercomputing to perform a large collection of independenttasks, while dealing with undependable processors. The adversary may cause theprocessors to return bogus results for tasks with certain probabilities, andmay cause a subset $F$ of the initial set of processors $P$ to crash. Theadversary is constrained in two ways. First, for the set of non-crashedprocessors $P-F$, the \emph{average} probability of a processor returning abogus result is inferior to $\frac{1}{2}$. Second, the adversary may crash asubset of processors $F$, provided the size of $P-F$ is bounded from below. Weconsider two models: the first bounds the size of $P-F$ by a fractionalpolynomial, the second bounds this size by a poly-logarithm. Both models yieldadversaries that are much stronger than previously studied. Our randomizedsynchronous algorithm is formulated for $n$ processors and $t$ tasks, with$n\le t$, where depending on the number of crashes each live processor is ableto terminate dynamically with the knowledge that the problem is solved withhigh probability. For the adversary constrained by a fractional polynomial, theround complexity of the algorithm is$O(\frac{t}{n^\varepsilon}\log{n}\log{\log{n}})$, its work is $O(t\log{n}\log{\log{n}})$ and message complexity is $O(n\log{n}\log{\log{n}})$. For thepoly-log constrained adversary, the round complexity is $O(t)$, work is $O(tn^{\varepsilon})$, %$O(t \, poly \log{n})$, and message complexity is$O(n^{1+\varepsilon})$ %$O(n \, poly \log{n})$. All bounds are shown to holdwith high probability.

Technical Report: Dealing with Undependable Workers in Decentralized Network Supercomputing