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# Computing minimum cycle bases in weighted partial 2-trees in linear time

Publikationstyp

Conference Paper

Publikationsdatum

2013

Sprache

English

TORE-URI

First published in

Number in series

8165 LNCS

Start Page

225

End Page

236

Citation

39th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2013)

Contribution to Conference

Publisher DOI

Scopus ID

We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis (MCB) in weighted partial 2-trees, i.e., graphs of treewidth two. The implicit representation can be made explicit in a running time that is proportional to the size of the MCB. 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 logn) space representation of an MCB in O(n log5 n) time. For the special case of partial 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].