Doerr, CarolaCarolaDoerrRamakrishna, G.G.RamakrishnaSchmidt, Jens M.Jens M.Schmidt2020-10-212020-10-21201339th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2013)http://hdl.handle.net/11420/7634We 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].enInformatikConference Paper10.1007/978-3-642-45043-3_20Other