期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2011
卷号：2011
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：In recent results the complexity of isomorphism testing on
graphs of bounded treewidth is improved to TC1 [GV06] and further to LogCFL [DTW10].
The computation of canonical forms or a canonical labeling provides more information than
isomorphism testing.
Whether canonization is in NC or even TC1 was stated as an open question in [Köb06].
Köbler and Verbitsky [KV08] give a TC2 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 [EJT10],
and techniques of Lindells tree canonization algorithm [Lin92].
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.
