Finding an optimal tree searching strategy in linear time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sorting and selection in posets
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Quantum search of partially ordered sets
Quantum Information & Computation
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
Sorting and Selection in Posets
SIAM Journal on Computing
The binary identification problem for weighted trees
Theoretical Computer Science
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We extend the binary search technique to searching in trees. We consider two models of queries: questions about vertices and questions about edges. We present a general approach to this sort of problem, and apply it to both cases, achieving algorithms constructing optimal decision trees. In the edge query model the problem is identical to the problem of searching in a special class of tree-like posets stated by Ben-Asher, Farchi and Newman [1]. Our upper bound on computation time, O(n^3 ), improves the previous best known O(n^4 log^3 n). In the vertex query model we show how to compute an optimal strategy much faster, in O(n) steps. We also present an almost optimal approximation algorithmfor another class of tree-like (and forest-like) partial orders.