STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
I. Schur, C.E. Shannon and Ramsey Numbers, a short story
Discrete Mathematics
Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey
Data Mining and Knowledge Discovery
On an Optimal Split Tree Problem
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Optimal binary decision trees for diagnostic identification problems
Optimal binary decision trees for diagnostic identification problems
Approximating Min Sum Set Cover
Algorithmica
Decision trees for entity identification: approximation algorithms and hardness results
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Improving access to organized information
Improving access to organized information
Approximating Optimal Binary Decision Trees
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximating Decision Trees with Multiway Branches
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
EvoWorkshops'03 Proceedings of the 2003 international conference on Applications of evolutionary computing
Decision-theoretic troubleshooting: Hardness of approximation
International Journal of Approximate Reasoning
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We consider the problem of constructing decision trees for entity identification from a given relational table. The input is a table containing information about a set of entities over a fixed set of attributes and a probability distribution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is to construct a decision tree that identifies each entity unambiguously by testing the attribute values such that the average number of tests is minimized. This classical problem finds such diverse applications as efficient fault detection, species identification in biology, and efficient diagnosis in the field of medicine. Prior work mainly deals with the special case where the input table is binary and the probability distribution over the set of entities is uniform. We study the general problem involving arbitrary input tables and arbitrary probability distributions over the set of entities. We consider a natural greedy algorithm and prove an approximation guarantee of O(rK ⋅ log N), where N is the number of entities and K is the maximum number of distinct values of an attribute. The value rK is a suitably defined Ramsey number, which is at most log K. We show that it is NP-hard to approximate the problem within a factor of Ω(log N), even for binary tables (i.e., K=2). Thus, for the case of binary tables, our approximation algorithm is optimal up to constant factors (since r2=2). In addition, our analysis indicates a possible way of resolving a Ramsey-theoretic conjecture by Erdös.