Finding an optimal tree searching strategy in linear time

Shay Mozes, Krzysztof Onak, Oren Weimann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We address the extension of the biliary search technique from sorted arrays and totally ordered sets to trees and tree-like partially ordered sets. As in the sorted array case, the goal is to minimize the number of queries required to find a target element in the worst case. However, while the optimal strategy for searching an array is straightforward (always query the middle element), the optimal strategy for searching a tree is dependent on the tree's structure and is harder to compute. We present an O(n)-time algorithm that finds the optimal strategy for binary searching a tree, improving the previous best O(n 3)-time algorithm. The significant improvement is due to a novel approach for computing subproblems, as well as a method for reusing parts of already computed subproblenis, and a lineartime transformation from a solution in the form of an edge-weighed tree into a solution in the form of a decision tree.

Original languageEnglish
Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages1096-1105
Number of pages10
StatePublished - 2008
Externally publishedYes
Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
Duration: 20 Jan 200822 Jan 2008

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference19th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CitySan Francisco, CA
Period20/01/0822/01/08

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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