TY - GEN

T1 - Approximation algorithms for optimal decision trees and adaptive TSP problems

AU - Gupta, Anupam

AU - Nagarajan, Viswanath

AU - Ravi, R.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955311994&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-14165-2_58

DO - 10.1007/978-3-642-14165-2_58

M3 - Conference contribution

AN - SCOPUS:77955311994

SN - 3642141641

SN - 9783642141645

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 690

EP - 701

BT - Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings

T2 - 37th International Colloquium on Automata, Languages and Programming, ICALP 2010

Y2 - 6 July 2010 through 10 July 2010

ER -