Download:
|
by Raymond Greenlaw, Teresa M. Przytycka
http://www.cs.armstrong.edu/greenlaw/research/treeranking.ps
Add To MetaCart
Abstract:
This paper places the optimal tree ranking problem in NC. A ranking is a labeling of the nodes with natural numbers such that if nodes u and v have the same label then there exists another node with a greater label on the path between them. An optimal ranking is a ranking in which the largest label assigned to any node is as small as possible among all rankings. An O(n) sequential algorithm is known. Researchers have speculated that this problem is P-complete. We show that for an n-node tree, one can compute an optimal ranking in O(log n) time using n
Citations
|
281
|
Parallel algorithms for shared-memory machines
– Karp, Ramachandran
- 1990
|
|
195
|
A taxonomy of problems with fast parallel algorithms
– Cook
- 1985
|
|
166
|
Efficient parallel algorithms
– Gibbons
- 1988
|
|
113
|
Parallel tree contraction and its applications
– Miller, Reif
- 1985
|
|
110
|
Fundamental Algorithms, volume 1 of The Art of Computer Programming
– Knuth
- 1968
|
|
88
|
A simple parallel tree contraction algorithm
– Abrahamson, Dadoun, et al.
- 1989
|
|
33
|
The accelerated centroid decomposition technique for optimal parallel tree evaluation in logarithmic time. Algon'thmica
– Cole, Vishkin
- 1988
|
|
21
|
A compendium of problems complete for P
– Greenlaw, Hoover, et al.
- 1991
|
|
14
|
Optimal node ranking of trees in linear time
– Schaffer
- 1989
|
|
11
|
Optimal node ranking of trees
– Iyer, Ratliff, et al.
- 1988
|
|
9
|
Efficient parallel algorithms for solving some tree problems
– He
- 1986
|
|
4
|
The complexity of two-way pushdown automata and recursive programs
– Rytter
- 1985
|
|
3
|
Super critical tree numbering and optimal tree ranking are in NC
– Torre, Greenlaw
- 1991
|
|
3
|
Parallel algorithms for ranking of trees
– Liang, Dhall, et al.
- 1990
|
|
3
|
Systematic methods for tree based parallel algorithm development
– Miller, Teng
- 1987
|
|
2
|
The optimal tree ranking problem is
– Przytycka
- 1991
|
|
1
|
Parallel Algorithms for Tree Construction and Related Problems
– Przytycka
- 1990
|
