Optimal Search on Some Game Trees
Journal of the ACM (JACM)
On computing functions with uncertainty
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Selection with monotone comparison costs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Randomized Approximation Algorithms for Query Optimization Problems on Two Processors
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
Sorting and Selection with Structured Costs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the competitive ratio of evaluating priced functions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Querying priced information in databases: The conjunctive case
ACM Transactions on Algorithms (TALG)
The hardness of the Expected Decision Depth problem
Information Processing Letters
A note on the size of minimal covers
Information Processing Letters
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)
Competitive Boolean function evaluation: Beyond monotonicity, and the symmetric case
Discrete Applied Mathematics
An optimal algorithm for querying priced information: monotone boolean functions and game trees
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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This paper focuses on competitive function evaluation in the context of computing with priced information. A function f is given together with a cost cx for each variable x of f. The cost cx has to be paid to read the value of x. The problem is to design algorithms that query the values of the variables sequentially in order to compute the function while trying to minimize the total cost incurred. Competitive analysis is employed to evaluate the performance of the algorithms. We describe a novel approach for devising efficient algorithms in this setting. We apply our approach to several classes of functions which have been studied in the literature of computing with priced information. In all cases considered, our approach provides algorithms that achieve better bounds than the best known algorithm for the same class of functions.More precisely, for the class of monotone boolean functions, we give a polynomial time algorithm with extremal competitiveness (k+l - √ min(k,l)) where k (l) denotes the minimum number of variables that one must read, in the worst case, in order to prove that the function under consideration evaluates to 1 (0). This dramatically improves upon the best known result which is an exponential time 2 max(k, l)-competitive algorithm. For the subclass of monotone boolean functions known as Threshold Trees we further improve our bounds and give a polynomial time algorithm with extremal competitive ratio 1.618 max(k, l).We then apply our methodology to classes of non-boolean functions. We consider the case of the so called Game Trees. We improve upon previously published results for this class of functions providing a polynomial time algorithm with extremal competitive ratio 1.5 γ(f), where γ(f) is a lower bound on the extremal competitive ratio of any deterministic algorithm.Finally, we consider the case when f is the function min (minimum). In this case, we are able to determine the optimal competitiveness for the problem. In fact we provide an algorithm with an (n-2)-competitive ratio, which matches the known lower bound.