Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Optimization techniques for queries with expensive methods
ACM Transactions on Database Systems (TODS)
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
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Selection with monotone comparison costs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
Two applications of information complexity
Proceedings of the thirty-fifth 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
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Finding optimal satisficing strategies for and-or trees
Artificial Intelligence
Sorting and selection with random costs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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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Let f be a function on a set of variables V. For each x ∈ V, let c(x) be the cost of reading the value of x. An algorithm for evaluating f is a strategy for adaptively identifying and reading a set of variables U ⊆ V whose values uniquely determine the value of f. We are interested in finding algorithms which minimize the cost incurred to evaluate f in the above sense. Competitive analysis is employed to measure the performance of the algorithms. We address two variants of the above problem. We consider the basic model in which the evaluation algorithm knows the cost c(x), for each x ∈ V. We also study a novel model where the costs of the variables are not known in advance and some preemption is allowed in the reading operations. This model has applications, for example, when reading a variable coincides with obtaining the output of a job on a CPU and the cost is the CPU time. For the model where the costs of the variables are known, we present a polynomial time algorithm with the best possible competitive ratio γcf for each function f that is representable by a threshold tree and for each fixed cost function c(⋅). Remarkably, the best-known result for the same class of functions is a pseudo-polynomial algorithm with competitiveness 2 γcf. Still in the same model, we introduce the Linear Programming Approach (LPA), a framework that allows the design of efficient algorithms for evaluating functions. We show that different implementations of this approach lead in general to the best algorithms known so far—and in many cases to optimal algorithms—for different classes of functions considered before in the literature. Via the LPA, we are able to determine exactly the optimal extremal competitiveness of monotone Boolean functions. Remarkably, the upper bound which leads to this result, holds for a much broader class of functions, which also includes the whole set of Boolean functions. We also show how to extend the LPA (together with these results) to the model where the costs of the variables are not known beforehand. In particular, we show how to employ the extended LPA to design a polynomial-time optimal (with respect to competitiveness) algorithm for the class of monotone Boolean functions representable by threshold trees.