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Author, Editor(s)

Author(s):

Arikati, Srinivasa Rao
Chaudhuri, Shiva
Zaroliagis, Christos

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BibTeX cite key*:

Arikati-Chaudhuri-Zaroliagis-98

Title

Title*:

All-Pairs Min-Cut in Sparse Networks

Journal

Journal Title*:

Journal of Algorithms

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Language:

English

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ISSN:

0196-6774

Vol, No, pp, Date

Volume*:

29

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Publishing Date:

1998

Pages*:

82-110

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(LaTeX) Abstract:

Algorithms are presented for the all-pairs min-cut problem in bounded
tree-width, planar and sparse networks. The approach used
is to preprocess the input $n$-vertex network so that, afterwards, the
value of a min-cut between any two vertices can be efficiently
computed. A tradeoff is shown between the preprocessing time and the time
taken to compute min-cuts subsequently. In particular, after
an $O(n\log n)$ preprocessing of a bounded tree-width network,
it is possible to find the value of a
min-cut between any two vertices in constant time. This implies that
for such networks the all-pairs min-cut problem can be solved
in time $O(n^2)$.
This algorithm is used in conjunction with a graph
decomposition technique of Frederickson to obtain algorithms for
sparse and planar networks. The running times depend upon a
topological property, $\gamma$, of the input network.
The parameter $\gamma$ varies between
1 and $\Theta(n)$; the algorithms perform well when $\gamma = o(n)$.
The value of a min-cut can be found in time $O(n + \gamma^2 \log
\gamma)$ and all-pairs min-cut can be solved in time $O(n^2 + \gamma^4
\log \gamma)$ for sparse networks. The corresponding running times
for planar networks are $O(n+\gamma \log \gamma)$ and $O(n^2 + \gamma^3
\log \gamma)$, respectively. The latter bounds depend on a result
of independent interest: outerplanar networks have small
``mimicking'' networks which are also outerplanar.

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MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Audience:

experts only

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BibTeX Entry:

@ARTICLE{Arikati-Chaudhuri-Zaroliagis-98,
AUTHOR = {Arikati, Srinivasa Rao and Chaudhuri, Shiva and Zaroliagis, Christos},
TITLE = {All-Pairs Min-Cut in Sparse Networks},
JOURNAL = {Journal of Algorithms},
YEAR = {1998},
VOLUME = {29},
PAGES = {82--110},
ISBN = {0196-6774},
}


Entry last modified by Uwe Brahm, 03/02/2010
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Editor(s)
Christos Zaroliagis
Created
02/25/1999 06:43:28 PM
Revisions
3.
2.
1.
0.
Editor(s)
Uwe Brahm
Uwe Brahm
Christos Zaroliagis
Christos Zaroliagis
Edit Dates
04.04.2000 11:11:03
30.03.99 22:40:50
25/02/99 19:13:42
25/02/99 18:43:28