Computing Prüfer codes efficiently in parallel

A Prüfer code of a labeled free tree with n nodes is a sequence of length n−2 constructed by the following sequential process: for i ranging from 1 to n−2 insert the label of the neighbor of the smallest remaining leaf into the ith position of the sequence, and then delete the leaf. Prüfer codes pro...

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Veröffentlicht in:Discrete Applied Mathematics Jg. 102; H. 3; S. 205 - 222
Hauptverfasser: Greenlaw, Raymond, Petreschi, Rossella
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Lausanne Elsevier B.V 15.06.2000
Amsterdam Elsevier
New York, NY
Schlagworte:
Applied sciences
Coding, codes
Combinatorics
Combinatorics. Ordered structures
EREW-PRAM algorithms
Exact sciences and technology
Graph theory
Information, signal and communications theory
Mathematics
Parallel algorithms
Prüfer codes
Sciences and techniques of general use
Signal and communications theory
Telecommunications and information theory
Trees
Trees
EREW-PRAM algorithms
Prüfer codes
Parallel algorithms
Labelled graph
Optimal time
Parallel algorithm
Tree(graph)
Prufer code
Code
labelled free tree
ISSN:0166-218X, 1872-6771
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Abstract A Prüfer code of a labeled free tree with n nodes is a sequence of length n−2 constructed by the following sequential process: for i ranging from 1 to n−2 insert the label of the neighbor of the smallest remaining leaf into the ith position of the sequence, and then delete the leaf. Prüfer codes provide an alternative to the usual representation of trees. We present an optimal O( log n) time, n/ log n processor EREW-PRAM algorithm for determining the Prüfer code of an n-node labeled chain and an O( log n) time, n processor EREW-PRAM algorithm for constructing the Prüfer code of an n-node labeled free tree. This resolves an open question posed by Wang et al. (IEEE Trans. Parallel Distributed Systems 8 (12) (1997) 1236–1240).
AbstractList A Prüfer code of a labeled free tree with n nodes is a sequence of length n−2 constructed by the following sequential process: for i ranging from 1 to n−2 insert the label of the neighbor of the smallest remaining leaf into the ith position of the sequence, and then delete the leaf. Prüfer codes provide an alternative to the usual representation of trees. We present an optimal O( log n) time, n/ log n processor EREW-PRAM algorithm for determining the Prüfer code of an n-node labeled chain and an O( log n) time, n processor EREW-PRAM algorithm for constructing the Prüfer code of an n-node labeled free tree. This resolves an open question posed by Wang et al. (IEEE Trans. Parallel Distributed Systems 8 (12) (1997) 1236–1240).
Author Greenlaw, Raymond
Petreschi, Rossella
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  givenname: Rossella
  surname: Petreschi
  fullname: Petreschi, Rossella
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  organization: Department of Computer Science, University of Rome “La Sapienza”, Via Salaria 113, Rome, 00198, Italy
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Cites_doi 10.1145/321812.321815
10.1016/B978-0-444-88071-0.50022-9
10.1109/71.640015
10.1145/322217.322232
10.1137/0217049
10.1007/BFb0040376
10.1016/B978-0-444-81504-0.50006-0
10.1007/BF02280884
10.1007/BF01762121
10.1016/0196-6774(89)90017-5
10.1137/0214061
10.1016/0304-3975(82)90011-1
10.1137/0134037
10.1093/oso/9780195085914.001.0001
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Issue 3
Keywords Trees
EREW-PRAM algorithms
Prüfer codes
Parallel algorithms
Labelled graph
Optimal time
Parallel algorithm
Tree(graph)
Prufer code
Code
labelled free tree
Language English
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Snippet A Prüfer code of a labeled free tree with n nodes is a sequence of length n−2 constructed by the following sequential process: for i ranging from 1 to n−2...
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SubjectTerms Applied sciences
Coding, codes
Combinatorics
Combinatorics. Ordered structures
EREW-PRAM algorithms
Exact sciences and technology
Graph theory
Information, signal and communications theory
Mathematics
Parallel algorithms
Prüfer codes
Sciences and techniques of general use
Signal and communications theory
Telecommunications and information theory
Trees
Title Computing Prüfer codes efficiently in parallel
URI https://dx.doi.org/10.1016/S0166-218X(99)00221-8
Volume 102
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