Title :
Parallel algorithms for ranking of trees
Author :
Liang, Y. ; Dhall, S.K. ; Lakshmivarahan, S.
Author_Institution :
Sch. of Electr. Eng. & Comput. Sci., Oklahoma Univ., OK, USA
Abstract :
Ranking a tree is defined as a mapping ρ of the nodes to the set {1, 2, . . .} such that if there is a path from u to v and ρ(u)=ρ(v) then there is a node w on the path from u to v such that ρ(w)>ρ(u). The highest number assigned to the node is called the rank number of the mapping. A mapping ρ with the smallest rank number is called optimal ranking. The best known serial algorithm takes O(n) time for the optimal node ranking. However, the problem of finding the optimal tree ranking appears to be highly sequential. It remains open whether it is in NC. The paper proposes a fast parallel algorithm for finding approximate optimal node ranking of trees using O(logn) steps with n2 processors on a CRCW PRAM and an efficient parallel algorithm using O(log2n) steps with n processors on a EREW model
Keywords :
computational complexity; parallel algorithms; trees (mathematics); CRCW PRAM; EREW model; mapping; nodes; optimal ranking; parallel algorithm; path; rank number; set; tree ranking; Algorithm design and analysis; Circuits; Communication networks; Computer science; Parallel algorithms; Particle separators; Phase change random access memory; Random access memory; Read-write memory; Tree graphs;
Conference_Titel :
Parallel and Distributed Processing, 1990. Proceedings of the Second IEEE Symposium on
Conference_Location :
Dallas, TX
Print_ISBN :
0-8186-2087-0
DOI :
10.1109/SPDP.1990.143502