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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Efficient Edge Splitting-Off Algorithms Maintaining All-Pairs Edge-Connectivities
verfasst von : Lap Chi Lau, Chun Kong Yung
Erschienen in: Integer Programming and Combinatorial Optimization
Verlag: Springer Berlin Heidelberg
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In this paper we present new edge splitting-off results maintaining all-pairs edge-connectivities of a graph. We first give an alternate proof of Mader’s theorem, and use it to obtain a deterministic
$\tilde{O}({r_{\max}}^2 \cdot n^2)$
-time complete edge splitting-off algorithm for unweighted graphs, where
r
max
denotes the maximum edge-connectivity requirement. This improves upon the best known algorithm by Gabow by a factor of
$\tilde{\Omega}(n)$
. We then prove a new structural property, and use it to further speedup the algorithm to obtain a randomized
$\tilde{O}(m + {r_{\max}}^3 \cdot n)$
-time algorithm. These edge splitting-off algorithms can be used directly to speedup various graph algorithms.