Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
An optimally efficient selection algorithm
Information Processing Letters
Binary tree algebraic computation and parallel algorithms for simple graphs
Journal of Algorithms
A simple parallel tree contraction algorithm
Journal of Algorithms
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Algorithms for a core and k-tree core of a tree
Journal of Algorithms
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
The k-centrum multi-faculty location problem
Discrete Applied Mathematics
Cost-Optimal Parallel Algorithms for the Tree Bisector and Related Problems
IEEE Transactions on Parallel and Distributed Systems
Wireless and Mobile Network Architectures
Wireless and Mobile Network Architectures
Finding a 2-Core of a Tree in Linear Time
SIAM Journal on Discrete Mathematics
On a unified architecture for video-on-demand services
IEEE Transactions on Multimedia
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
Self-Stabilizing Clustering of Tree Networks
IEEE Transactions on Computers
Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
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Let T=(V, E) be an edge-weighted tree with |V|=n vertices embedded in the Euclidean plane. Let {\hbox{\rlap{I}\kern 2.0pt{\hbox{E}}}} denote the set of all points on the edges of T. Let X and Y be two subsets of {\hbox{\rlap{I}\kern 2.0pt{\hbox{E}}}} and let r be a positive real number. A subset D\subseteq X is an X/Y/r{\hbox{-}}dominating setif every point in Y is within distance r of a point in D. The X/Y/r{\hbox{-}}dominating setproblem is to find an X/Y/r{\hbox{-}}{\rm{dominating}} set D^* with minimum cardinality. Let p\ge 1 be an integer. The X/Y/p{\hbox{-}}centerproblem is to find a subset C^*\subseteq X of p points such that the maximum distance of any point in Y from C^* is minimized. Let X and Y be either V or {\hbox{\rlap{I}\kern 2.0pt{\hbox{E}}}}. In this paper, efficient parallel algorithms on the EREW PRAM are first presented for the X/Y/r{\hbox{-}}{\rm{dominating}} set problem. The presented algorithms require O(\log^2n) time for all cases of X and Y. Parallel algorithms on the EREW PRAM are then developed for the X/Y/p{\hbox{-}}{\rm{center}} problem. The presented algorithms require O(\log^3n) time for all cases of X and Y. Previously, sequential algorithms for these two problems had been extensively studied in the literature. However, parallel solutions with polylogarithmic time existed only for their special cases. The algorithms presented in this paper are obtained by using an interesting approach which we call the dependency-tree approach. Our results are examples of parallelizing sequential dynamic-programming algorithms by using the approach.