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• W2152124311 abstract "We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of m possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight O(logm)-approximation algorithm. We also consider a more substantial generalization, the Adaptive TSP problem, which can be used to model switching costs between tests in the optimal decision tree problem. Given an underlying metric space, a random subset S of cities is drawn from a known distribution, but S is initially unknown to us—we get information about whether any city is in S only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset S while minimizing the expected distance traveled? For this adaptive TSP problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless we can improve the approximation guarantees for the well-known group Steiner tree problem." @default.
• W2152124311 created "2016-06-24" @default.
• W2152124311 creator A5051270969 @default.
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• W2152124311 creator A5087844619 @default.
• W2152124311 date "2010-01-01" @default.
• W2152124311 modified "2023-10-18" @default.
• W2152124311 title "Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems" @default.
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• W2152124311 doi "https://doi.org/10.1007/978-3-642-14165-2_58" @default.
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