Edge ranking of graphs is hard
Discrete Applied Mathematics
Optimal edge ranking of trees in linear time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
On minimum edge ranking spanning trees
Journal of Algorithms
Edge ranking of weighted trees
Discrete Applied Mathematics
Efficient Parallel Query Processing by Graph Ranking
Fundamenta Informaticae
Minimum average cost testing for partially ordered components
IEEE Transactions on Information Theory
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice 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
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 consider a problem of searching an element in a partially ordered set (poset). The goal is to find a search strategy which minimizes the number of comparisons. Ben-Asher, Farchi and Newman considered a special case where the partial order has the maximum element and the Hasse diagram is a tree (tree-like posets) and they gave an O(n^4log^3n)-time algorithm for finding an optimal search strategy for such a partial order. We show that this problem is equivalent to finding edge ranking of a simple tree corresponding to the Hasse diagram, which implies the existence of a linear-time algorithm for this problem. Then we study a more general problem, namely searching in any partial order with maximum element. We prove that such a generalization is hard, and we give an O(lognlog(logn))-approximate polynomial-time algorithm for this problem.