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On an Optimal Split Tree Problem

  • S. Rao Kosaraju
  • Teresa M. Przytycka
  • Ryan Borgstrom
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

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.

Keywords

Greedy Algorithm Search Tree Internal Node Approximation Ratio SIAM Journal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • S. Rao Kosaraju
    • 1
  • Teresa M. Przytycka
    • 2
  • Ryan Borgstrom
  1. 1.Department of Computer ScienceJohns Hopkins UniversityUSA
  2. 2.Department of BiophysicsJohns Hopkins School of MedicineUSA

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