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MPI-I-95-1-013

Efficient computation of implicit representations of sparse graphs (revised version)

Arikati, Srinivasa R. and Maheshwari, Anil and Zaroliagis, Christos D.

MPI-I-95-1-013. June 1995, 16 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
The problem of finding an implicit representation for a graph
such that vertex adjacency can be tested quickly is
fundamental to all graph algorithms. In particular, it
is possible to represent sparse graphs on $n$ vertices
using $O(n)$ space such that vertex adjacency is tested
in $O(1)$ time. We show here how to construct such a
representation efficiently by providing simple and optimal
algorithms, both in a sequential and a parallel setting.
Our sequential algorithm runs in $O(n)$ time.
The parallel algorithm runs in $O(\log n)$ time using
$O(n/{\log n})$ CRCW PRAM processors, or in $O(\log n\log^*n)$
time using $O(n/\log n\log^*n)$ EREW PRAM processors.
Previous results for this problem
are based on matroid partitioning and thus have a high complexity.
Acknowledgement:
References to related material:

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1995-1-013
Hide details for BibTeXBibTeX
@TECHREPORT{ArikatiMaheshwariZaroliagis95,
  AUTHOR = {Arikati, Srinivasa R. and Maheshwari, Anil and Zaroliagis, Christos D.},
  TITLE = {Efficient computation of implicit representations of sparse graphs (revised version)},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-95-1-013},
  MONTH = {June},
  YEAR = {1995},
  ISSN = {0946-011X},
}