TY - GEN

T1 - Finding an optimal tree searching strategy in linear time

AU - Mozes, Shay

AU - Onak, Krzysztof

AU - Weimann, Oren

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58449086080&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:58449086080

SN - 9780898716474

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1096

EP - 1105

BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms

T2 - 19th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 20 January 2008 through 22 January 2008

ER -