In this paper, we prove new upper bounds on the complexity of the certified write-all problem with respect to an adaptive adversary. Our strongest result is that for any ǫ > 0, there exists an O(p 1+ǫ) work algorithm for the p-processor p-memory cell write-all. We also give a randomized O(p 2 log p) work algorithm for a p-processor p 2-memory cell write-all.

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We are interested in designing efficient data structures for a shared memory multiprocessor.In this paper we focus on the union-find data structure. Our machine model is asynchronous and allows stopping faults. Thus we require our solutions to the data structure problem have the wait-free property, meaning that each thread continues to make progress on its operations, independent of the speeds of the other threads. In this model efficiency is best measured in terms of the total number of instructions used to perform a sequence of data structure operations, the work performed by the processors. We give a wait-free implementation of an efficient algorithm for union-find. In addition we show that the worst case performance of the algorithm can be improved by simulating a synchronized algorithm, or by simulating a larger machine if the data structure requests support sufficient parallelism. Our solutions apply to a much more general adversary model than has been considered by other authors.

This paper demonstrates that Shamir's scheme [10] is not secure against certain forms of cheating. A small modification to his scheme retains the security and efficiency of the original, is secure against these forms of cheating, and preserves the property that its security does not depend on any unproven assumptions such as the intractability of computing number-theoretic functions.