Computing with unreliable information
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Searching games with errors---fifty years of coping with liars
Theoretical Computer Science
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Noisy binary search and its applications
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Noisy sorting without resampling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sorting and Selection with Imprecise Comparisons
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ACM Transactions on Algorithms (TALG)
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Assume we are interested in solving a computational task, e.g., sorting n numbers, and we only have access to an unreliable primitive operation, for example, comparison between two numbers. Suppose that each primitive operation fails with probability at most p and that repeating it is not helpful, as it will result in the same outcome. Can we still approximately solve our task with probability 1-f(p) for a function f that goes to 0 as p goes to 0? While previous work studied sorting in this model, we believe this model is also relevant for other problems. We - find the maximum of n numbers in O(n) time, - solve 2D linear programming in O(n log n) time, - approximately sort n numbers in O(n2) time such that each number's position deviates from its true rank by at most O(log n) positions, - find an element in a sorted array in O(log n log log n) time. Our sorting result can be seen as an alternative to a previous result of Braverman and Mossel (SODA, 2008) who employed the same model. While we do not construct the maximum likelihood permutation, we achieve similar accuracy with a substantially faster running time.