Problems complete for deterministic logarithmic space
Journal of Algorithms
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
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
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
On the nonuniform complexity of the graph isomorphism problem
Complexity theory
Circuits, matrices, and nonassociative computation
Journal of Computer and System Sciences
Symmetric logspace is closed under complement
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A compendium of problems complete for symmetric logarithmic space
Computational Complexity
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The Complexity of Graph Isomorphism for Colored Graphs with Color Classes of Size 2 and 3
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
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
A Note on the Hardness of Tree Isomorphism
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
On the hardness of graph isomorphism
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Counting quantifiers, successor relations, and logarithmic space
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
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
The space complexity of k-tree isomorphism
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Reductions to graph isomorphism
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Four lessons in versatility or how query languages adapt to the web
Semantic techniques for the web
A logspace algorithm for partial 2-tree canonization
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Isomorphism of regular trees and words
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Canonizing hypergraphs under abelian group action
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
On hypergraph and graph isomorphism with bounded color classes
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects 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
Progressive solutions: a simple but efficient dominance rule for practical RCPSP
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The isomorphism problem for k-trees is complete for logspace
Information and Computation
Restricted space algorithms for isomorphism on bounded treewidth graphs
Information and Computation
Isomorphism of regular trees and words
Information and Computation
On the resolution complexity of graph non-isomorphism
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is many-one complete for several complexity classes within NC2. In particular we show that tree isomorphism, when trees are encoded as strings, is NC1-hard under AC0-reductions. NC1- completeness thus follows from Buss's NC1 upper bound. By contrast, we prove that testing isomorphism of two trees encoded as pointer lists is L-complete. Concerning colored graphs we show that the isomorphism problem for graphs with color multiplicities 2 and 3 is complete for symmetric logarithmic space SL under many-one reductions. This result improves the existing upper bounds for the problem. We also show that the graph automorphism problem for colored graphs with color classes of size 2 is equivalent to deciding whether a graph has more than a single connected component and we prove that for color classes of size 3 the graph automorphism problem is contained in SL.