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Computing minimum cycle bases in weighted partial 2-trees in linear time
Publikationstyp
Journal Article
Date Issued
2014
Sprache
English
Author(s)
TORE-URI
Volume
18
Issue
3
Start Page
325
End Page
346
Citation
Journal of Graph Algorithms and Applications (2014)
Publisher DOI
Scopus ID
We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis in weighted partial 2-trees (i.e., graphs of treewidth at most two) with non-negative edge-weights. The implicit representation can be made explicit in a running time that is proportional to the size of the minimum cycle basis. For planar graphs, Borradaile, Sankowski, and Wulff-Nilsen [Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time, FOCS 2010] showed how to compute an implicit O(n log n) space representation of an minimum cycle basis in O(n log5 n) time. For the special case of par-tial 2-trees, our algorithm improves this result to linear time and space. Such an improvement was achieved previously only for outerplanar graphs. [Liu and Lu: Minimum Cycle Bases of Weighted Outerplanar Graphs, IPL 110:970-974, 2010].
DDC Class
510: Mathematik