Height restricted optimal binary trees
SIAM Journal on Computing
A new proof of the Garsia-Wachs algorithm
Journal of Algorithms
Elements of information theory
Elements of information theory
A Fast Algorithm for Optimum Height-Limited Alphabetic Binary Trees
SIAM Journal on Computing
The Optimal Alphabetic Tree Problem Revisited
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
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
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Decision trees for entity identification: Approximation algorithms and hardness results
ACM Transactions on Algorithms (TALG)
On the complexity of searching in trees and partially ordered structures
Theoretical Computer Science
Approximation algorithms for stochastic orienteering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Adaptive submodularity: theory and applications in active learning and stochastic optimization
Journal of Artificial Intelligence Research
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We introduce and study a problem that we refer to as the optimal split tree problem. The problem generalizes a number of problems including two classical tree construction problems including the Huffman tree problem and the optimal alphabetic tree. We show that the general split tree problem is NP-complete and analyze a greedy algorithm for its solution. We show that a simple modification of the greedy algorithm guarantees O(log n) approximation ratio. We construct an example for which this algorithm achieves Ω(log n/log log n) approximation ratio. We show that if all weights are equal and the optimal split tree is of depth O(log n). then the greedy algorithm guarantees O(log n/log log n) approximation ratio. We also extend our approximation algorithm to the construction of a search tree for partially ordered sets.