An O(nlogn)-size fault-tolerant sorting network (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Least adaptive optimal search with unreliable tests
Theoretical Computer Science
Least Adaptive Optimal Search with Unreliable Tests
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
On a multidimensional search problem (Preliminary Version)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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We consider the problem of identifying an unknown value x&egr;{1,2,...,n} using only comparisons of x to constants when as many as E of 'the comparisons may receive erroneous answers. For a continuous analogue of this problem we show that there is a unique strategy that is optimal in the worst case. This strategy for the continuous problem is then shown to yield a strategy for the original discrete problem that uses log2n+E.log2log2n+O(E.log2E) comparisons in the worst case. This number is shown to be optimal even if arbitrary “Yes-No” questions are allowed. We show that a modified version of this search problem with errors is equivalent to the problem of finding the minimal root of a set of increasing functions. The modified version is then also shown to be of complexity log2n+E.log2log2n+0(E.log2E).