max planck institut
informatik
informatik
MPI-I-98-1-009. April 1998, 18 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry
Abstract in LaTeX format:
We study the problem of maintaining the distances and the shortest
paths from a source node in a directed graph with arbitrary arc
weights, when weight updates of arcs are performed. We propose
algorithms that work for any digraph and have optimal space
requirements and query time. If a negative--length cycle is introduced
during weight decrease operations it is detected by the algorithms. The
proposed algorithms explicitly deal with zero--length cycles. The cost
of update operations depends on the class of the considered digraph
and on the number of the output updates. We show that, if the digraph
has a $k$-bounded accounting function (as in the case of digraphs with
genus, arboricity, degree, treewidth or pagenumber bounded by $k$) the
update procedures require $O(k\cdot n\cdot \log n)$ worst case
time. In the case of digraphs with $n$ nodes and $m$ arcs
$k=O(\sqrt{m})$, and hence we obtain $O(\sqrt{m}\cdot n \cdot \log n)$
worst case time per operation, which is better for a factor of
$O(\sqrt{m} / \log n)$ than recomputing everything from scratch after
each input update.
If we perform also insertions and deletions of arcs all the above
bounds become amortized.
Acknowledgement:
References to related material:
| To download this research report, please select the type of document that fits best your needs. | Attachement Size(s): |
|---|---|
| 549 KBytes | |
| Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView | |
BibTeX