On an edge ranking problem of trees and graphs
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 binary searching with non-uniform costs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On minimum edge ranking spanning trees
Journal of Algorithms
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
Efficient dynamic programming using quadrangle inequalities
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the hardness of the minimum height decision tree problem
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
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
Finding an optimal tree searching strategy in linear time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Edge ranking and searching in partial orders
Discrete Applied Mathematics
Edge ranking of weighted trees
Discrete Applied Mathematics
On the complexity of searching in trees: average-case minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Minimum average cost testing for partially ordered components
IEEE Transactions on Information Theory
| Hi-index | 5.23 |
The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a vertex in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T-e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. Moreover, for the degree 2 case, we significantly improve the straightforward O(n^3) dynamic programming approach, and provide an O(n^2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn.