NDLI: Finding minimum congestion spanning trees

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Finding minimum congestion spanning trees

Content Provider	ACM Digital Library
Author	Werneck, Renato Setubal, Joo da Conceico, Arlindo
Copyright Year	2000
Abstract	Given a weighted graph G = (V, E), a positive integer $\textit{k},$ and a penalty function $\textit{wp},$ we want to find $\textit{k}$ spanning trees on $\textit{G},$ not necessarily disjoint, of minimum total weight, such that the weight of each edge is subject to a penalty given by $\textit{wp}$ if it belongs to more than one tree. The objective function to be minimized is $Σ\textit{e∈EWe(ie)},$ where $\textit{ie}$ is the number of times edge e appears in the solution and We(ie) = iewp(e, ie) is the aggregate cost of using edge e ie times. For the case when $\textit{We}$ is weakly convex, which should have wide application in congestion problems, we present a polynomial time algorithm; the algorithm's complexity is quadratic in $\textit{k}.$ We also present two heuristics with complexity linear in $\textit{k}.$ In an experimental study we show that these heuristics are much faster than the exact algorithm also in practice. These experiments present a diverse combination of input families (four), varying $\textit{k}$ (up to 1000), and penalty functions (two). In most inputs tested the solutions given by the heuristics were within 1% of optimal or much better, especially for large $\textit{k}.$ The worst quality observed was 3.2% of optimal.
File Format	PDF
ISSN	10846654
e-ISSN	10846654
DOI	10.1145/351827.384253
Journal	Journal of Experimental Algorithmics (JEA)
Volume Number	5
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2000-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science

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