Max-Planck-Institut für Informatik
max planck institut
mpii logo Minerva of the Max Planck Society


Shortest paths in digraphs of small treewidth part II: optimal parallel algirithms

Chaudhuri, Shiva and Zaroliagis, Christos D.

MPI-I-95-1-021. August 1995, 20 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We consider the problem of preprocessing an $n$-vertex digraph with
real edge weights so that subsequent queries for the shortest path or distance
between any two vertices can be efficiently answered.
We give parallel algorithms for the EREW PRAM model of computation
that depend on the {\em treewidth} of
the input graph. When the treewidth is a constant, our algorithms
can answer distance queries in $O(\alpha(n))$ time using a single
processor, after a preprocessing of $O(\log^2n)$ time and $O(n)$ work,
where $\alpha(n)$ is the inverse of Ackermann's function.
The class of constant treewidth graphs
contains outerplanar graphs and series-parallel graphs, among
others. To the best of our knowledge, these
are the first parallel algorithms which achieve these bounds
for any class of graphs except trees.
We also give a dynamic algorithm which, after a change in
an edge weight, updates our data structures in $O(\log n)$ time
using $O(n^\beta)$ work, for any constant $0 < \beta < 1$.
Moreover, we give an algorithm of independent interest:
computing a shortest path tree, or finding a negative cycle in
$O(\log^2 n)$ time using $O(n)$ work.
References to related material:

To download this research report, please select the type of document that fits best your needs.Attachement Size(s): KBytes; 236 KBytes
Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView
URL to this document:
Hide details for BibTeXBibTeX
  AUTHOR = {Chaudhuri, Shiva and Zaroliagis, Christos D.},
  TITLE = {Shortest paths in digraphs of small treewidth part II: optimal parallel algirithms},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-95-1-021},
  MONTH = {August},
  YEAR = {1995},
  ISSN = {0946-011X},