On an Optimal Split Tree Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)


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 \( \Omega \left( {\frac{{\log n}} {{\log \log n}}} \right) \) 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 \( \Omega \left( {\frac{{\log n}} {{\log \log n}}} \right) \) approximation ratio. We also extend our approximation algorithm to the construction of a search tree for partially ordered sets.


Greedy Algorithm Search Tree Internal Node Approximation Ratio SIAM Journal 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Department of Computer ScienceJohns Hopkins UniversityUSA
  2. 2.Department of BiophysicsJohns Hopkins School of MedicineUSA

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