Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A logspace algorithm for tree canonization (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Efficient parallel algorithms for tree-decomposition and related problems
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Planar Graph Isomorphism is in Log-Space
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Isomorphism Problem for k-Trees Is Complete for Logspace
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
A logspace algorithm for partial 2-tree canonization
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
From invariants to canonization in parallel
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Logspace Versions of the Theorems of Bodlaender and Courcelle
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
The isomorphism problem for k-trees is complete for logspace
Information and Computation
The complexity of mining maximal frequent subgraphs
Proceedings of the 32nd symposium on Principles of database systems
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In recent results the complexity of isomorphism testing on graphs of bounded treewidth is improved to TC1 [17] and further to LogCFL [11]. 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 [18]. Köbler and Verbitsky [20] 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 [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.