Randomized algorithms
Matching nuts and bolts faster
Information Processing Letters
Matching nuts and bolts in O(n log n) time
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Query strategies for priced information (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Sorting and Selection with Structured Costs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A new strategy for querying priced information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the competitive ratio of evaluating priced functions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Playing games in many possible worlds
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
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)
An optimal algorithm for querying priced information: monotone boolean functions and game trees
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Where's the winner? max-finding and sorting with metric costs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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We consider the problem of selecting the rth-smallest element from a list of n elements under a model where the comparisons may have different costs depending on the elements being compared. This model was introduced by [3] and is realistic in the context of comparisons between complex objects. An important special case of this general cost model is one where the comparison costs are monotone in the sizes of the elements being compared. This monotone cost model covers most "natural" cost models that arise and the selection problem turns out to be the most challenging one among the usual problems for comparison-based algorithms. We present an O(log2 n)-competitive algorithm for selection under the monotone cost model. This is in contrast to an Ω(n) lower bound that is known for arbitrary comparison costs. We also consider selection under a special case of monotone costs --- the min model where the cost of comparing two elements is the minimum of the sizes. We give a randomized O(1)-competitive algorithm for the min model.