Sorting and recognition problems for ordered sets
SIAM Journal on Computing
Search in an ordered array having variable probe cost
SIAM Journal on Computing
Optimal on-line decremental connectivity in trees
Information Processing Letters
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
SIAM Journal on Computing
Communications of the ACM
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
Searching in random partially ordered sets
Theoretical Computer Science - Latin American theorotical informatics
Generalization of Binary Search: Searching in Trees and Forest-Like Partial Orders
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the Huffman and alphabetic tree problem with general cost functions
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Binary identification problems for weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Searching in dynamic tree-like partial orders
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
On the complexity of searching in trees and partially ordered structures
Theoretical Computer Science
The binary identification problem for weighted trees
Theoretical Computer Science
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We address the extension of the binary 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(n3)-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 subproblems, and a linear-time transformation from a solution in the form of an edge-weighed tree into a solution in the form of a decision tree.