In recent results the complexity of isomorphism testing on graphs of bounded treewidth is improved to TC1 [17] and further to [11]. The computation of canonical forms or a canonical labeling provides more information than isomorphism testing. Whether canonization is in or even TC1 was stated as an open question in [18]. Köbler and Verbitsky [20] give a canonical labeling algorithm. We show that a canonical labeling can be computed in AC1. This is based on several ideas, e.g. that approximate tree decompositions of logarithmic depth can be obtained in logspace [15], and techniques of Lindells tree canonization algorithm [22]. We define recursively what we call a minimal description which gives with respect to some parameters in a logarithmic number of levels a canonical invariant together with an arrangement of all vertices. From this we compute a canonical labeling. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Wagner, F. (2011). Graphs of bounded treewidth can be canonized in AC1. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6651 LNCS, pp. 209–222). https://doi.org/10.1007/978-3-642-20712-9_16
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