A taxonomy of problems with fast parallel algorithms
Information and Control
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Parallel tree contraction part 2: further applications
SIAM Journal on Computing
A logspace algorithm for tree canonization (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Journal of Algorithms
Counting quantifiers, successor relations, and logarithmic space
Journal of Computer and System Sciences - special issue on complexity theory
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Completeness results for graph isomorphism
Journal of Computer and System Sciences
The complexity of planarity testing
Information and Computation
On the Hardness of Graph Isomorphism
SIAM Journal on Computing
Computing Automorphism Groups of Chordal Graphs Whose Simplicial Components Are of Small Size
IEICE - Transactions on Information and Systems
Undirected connectivity in log-space
Journal of the ACM (JACM)
Counting Graph Isomorphisms among Chordal Graphs with Restricted Clique Number
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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
Information and Computation
The space complexity of k-tree isomorphism
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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
Graphs of bounded treewidth can be canonized in AC1
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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
On the isomorphism problem for decision trees and decision lists
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We show that, for k constant, k-tree isomorphism can be decided in logarithmic space by giving an O(klogn) space canonical labeling algorithm. The algorithm computes a unique tree decomposition, uses colors to fully encode the structure of the original graph in the decomposition tree and invokes Lindell@?s tree canonization algorithm. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for k-trees are all complete for deterministic logspace. Completeness for logspace holds even for simple structural properties of k-trees. We also show that a variant of our canonical labeling algorithm runs in time O((k+1)!n), where n is the number of vertices, yielding the fastest known FPT algorithm for k-tree isomorphism.