Information and Computation
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Complexity of searching an immobile hider in a graph
Discrete Applied Mathematics
Optimal constructions of hybrid algorithms
Journal of Algorithms
The number of cycle lengths in graphs of given minimum degree and girth
Discrete Mathematics
The ultimate strategy to search on m rays?
Theoretical Computer Science
On the optimality of a simple strategy for searching graphs
International Journal of Game Theory
Theoretical Computer Science
Journal of Scheduling
Pronunciation modeling for improved spelling correction
ACL '02 Proceedings of the 40th Annual Meeting on Association for Computational Linguistics
An improved error model for noisy channel spelling correction
ACL '00 Proceedings of the 38th Annual Meeting on Association for Computational Linguistics
A Note on Bipartite Graphs Without 2k-Cycles
Combinatorics, Probability and Computing
Scheduling search procedures: The wheel of fortune
Journal of Scheduling
The Interplay of Optimization and Machine Learning Research
The Journal of Machine Learning Research
Linear Programs for Hypotheses Selection in Probabilistic Inference Models
The Journal of Machine Learning Research
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Suppose that we are given n mutually exclusive hypotheses, m mutually exclusive possible observations, the conditional probabilities for each of these observations under each hypothesis, and a method to probe each hypothesis whether it is the true one. We consider the problem of efficient searching for the true (target) hypothesis given a particular observation. Our objective is to minimize the expected search cost for a large number of instances, and for the worst-case distribution of targets. More precisely, we wish to rank the hypotheses so that probing them in the chosen order is optimal in this sense. Costs grow monotonic with the number of probes. While it is straightforward to formulate this problem as a linear program, we can solve it in polynomial time only after a certain reformulation: We introduce mn^2 the so-called rank variables and arrive at another linear program whose solution can be translated afterwards into an optimal mixed strategy of low description complexity: For each observation, at most n rankings, i.e., permutations of hypotheses, appear with positive probabilities. Dimensionality arguments yield further combinatorial bounds. Possible applications of the optimization goal are discussed.