Computational geometry: an introduction
Computational geometry: an introduction
Efficient parallel algorithms
SIAM Journal on Computing
A simple parallel tree contraction algorithm
Journal of Algorithms
Introduction to algorithms
On optimal parallel computations for sequences of brackets
Theoretical Computer Science
An introduction to parallel algorithms
An introduction to parallel algorithms
Finding level-ancestors in trees
Journal of Computer and System Sciences
Parallel algorithm for finding a core of a tree network
Information Processing Letters
Efficient algorithms for finding a core of a tree with a specified length
Journal of Algorithms
Finding a k-Tree Core and a k-Tree Center of a Tree Network in Parallel
IEEE Transactions on Parallel and Distributed Systems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Parallel Algorithms for the Tree Bisector Problem and Applications
ICPP '99 Proceedings of the 1999 International Conference on Parallel Processing
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
Efficient Algorithms for Two Generalized 2-Median Problems on Trees
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Finding r-Dominating Sets and p-Centers of Trees in Parallel
IEEE Transactions on Parallel and Distributed Systems
Efficient algorithms for a constrained k-tree core problem in a tree network
Journal of Algorithms
Improved algorithms for the minmax-regret 1-center and 1-median problems
ACM Transactions on Algorithms (TALG)
Efficient algorithms for two generalized 2-median problems and the group median problem on trees
Theoretical Computer Science
Efficient algorithms for a constrained k-tree core problem in a tree network
Journal of Algorithms
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An edge is a bisector of a simple path if it contains the middle point of the path. Let T=(V, E) be a tree. Given a source vertex s \in V, the single-source tree bisector problem is to find, for every vertex v \in V, a bisector of the simple path from s to v. The all-pairs tree bisector problem is to find for, every pair of vertices u, v \in V, a bisector of the simple path from u to v. In this paper, it is first shown that solving the single-source tree bisector problem of a weighted tree has a time lower bound \Omega(n \log n) in the sequential case. Then, efficient parallel algorithms are proposed on the EREW PRAM for the single-source and all-pairs tree bisector problems. Two O(\log n) time single-source algorithms are proposed. One uses O(n) work and is for unweighted trees. The other uses O(n \log n) work and is for weighted trees. Previous algorithms for the single-source problem could achieve the same time O(\log n) and the same optimal work, O(n) for unweighted trees and O(n \log n) for weighted trees, on the CRCW PRAM. The contribution of our single-source algorithms is the improvement from CRCW to EREW. One all-pairs parallel algorithm is proposed. It requires O( \log n) time using O(n^2) work. All the proposed algorithms are cost-optimal. Efficient tree bisector algorithms have practical applications to several location problems on trees. Using the proposed algorithms, efficient parallel solutions for those problems are also presented.