On an Optimal Split Tree Problem

  • Authors:
  • S. Rao Kosaraju;Teresa M. Przytycka;Ryan S. Borgstrom

  • Affiliations:
  • -;-;-

  • Venue:
  • WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
  • Year:
  • 1999

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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(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.