A taxonomy of problems with fast parallel algorithms
Information and Control
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
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
PP is as hard as the polynomial-time hierarchy
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
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
Journal of the ACM (JACM)
On a New High Dimensional Weisfeiler-Lehman Algorithm
Journal of Algebraic Combinatorics: An International Journal
Isomorphism testing for embeddable graphs through definability
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Moderately Exponential Bound for Graph Isomorphism
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Alogtime Algorithms for Tree Isomorphism, Comparison, and Canonization
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism for graphs embeddable on the projective plane
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Completeness results for graph isomorphism
Journal of Computer and System Sciences
On the Hardness of Graph Isomorphism
SIAM Journal on Computing
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Parallel algorithms for permutation groups and graph isomorphism
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A Las Vegas - NC algorithm for isomorphism of graphs with bounded multiplicity of eigenvalues
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
No better ways to generate hard NP instances than picking uniformly at random
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
On hypergraph and graph isomorphism with bounded color classes
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Automorphisms of finite rings and applications to complexity of problems
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Graph Edit Distance without Correspondence from Continuous-Time Quantum Walks
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
On the Complexity of Matroid Isomorphism Problems
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Computational complexity of reconstruction and isomorphism testing for designs and line graphs
Journal of Combinatorial Theory Series A
Graphs of bounded treewidth can be canonized in AC1
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
| Hi-index | 0.00 |
Graph isomorphism (GI) is one of the few remaining problems in NP whose complexity status couldn't be solved by classifying it as being either NP-complete or solvable in P. Nevertheless, efficient (polynomial-time or even NC) algorithms for restricted versions of GI have been found over the last four decades. Depending on the graph class, the design and analysis of algorithms for GI use tools from various fields, such as combinatorics, algebra and logic. In this paper, we collect several complexity results on graph isomorphism testing and related algorithmic problems for restricted graph classes from the literature. Further, we provide some new complexity bounds (as well as easier proofs of some known results) and highlight some open questions.