Query strategies for priced information (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Selection with monotone comparison costs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Sorting and Selection with Structured Costs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Sorting and selection with random costs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
On the competitive ratio of evaluating priced functions
Journal of the ACM (JACM)
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Traditionally, a fundamental assumption in evaluating the performance of algorithms for sorting and selection has been that comparing any two elements costs one unit (of time, work, etc.); the goal of an algorithm is to minimize the total cost incurred. However, a body of recent work has attempted to find ways to weaken this assumption – in particular, new algorithms have been given for these basic problems of searching, sorting and selection, when comparisons between different pairs of elements have different associated costs. In this paper, we further these investigations, and address the questions of max-finding and sorting when the comparison costs form a metric; i.e., the comparison costs cuv respect the triangle inequality cuv + cvw ≥ cuw for all input elements u,v and w. We give the first results for these problems – specifically, we present An O(log n)-competitive algorithm for max-finding on general metrics, and we improve on this result to obtain an O(1)-competitive algorithm for the max-finding problem in constant dimensional spaces. An O(log2n)-competitive algorithm for sorting in general metric spaces. Our main technique for max-finding is to run two copies of a simple natural online algorithm (that costs too much when run by itself) in parallel. By judiciously exchanging information between the two copies, we can bound the cost incurred by the algorithm; we believe that this technique may have other applications to online algorithms.