Applications of combinatorial designs in computer science
ACM Computing Surveys (CSUR)
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
Faster isomorphism testing of strongly regular graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Graph isomorphism testing without numerics for graphs of bounded eigenvalue multiplicity
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Algorithm for Graph Isomorphism
Journal of the ACM (JACM)
On the nlog n isomorphism technique (A Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Computational complexity and the classification of finite simple groups
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Isomorhism of Hypergraphs of Low Rank in Moderately Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs
IEEE Transactions on Information Theory
Authentication and secrecy codes for equiprobable source probability distributions
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Combinatorial Designs for Authentication and Secrecy Codes
Foundations and Trends in Communications and Information Theory
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Quasipolynomial-time canonical form for steiner designs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line graphs of t-(v,k,@l) designs. For this class of highly regular graphs, we obtain a worst-case running time of O(v^l^o^g^v^+^O^(^1^)) for bounded parameters t, k, @l. In a first step, our approach makes use of the Babai-Luks algorithm to compute canonical forms of t-designs. In a second step, we show that t-designs can be reconstructed from their line graphs in polynomial-time. The first is algebraic in nature, the second purely combinatorial. For both, profound structural knowledge in design theory is required. Our results extend earlier complexity results about isomorphism testing of graphs generated from Steiner triple systems and block designs.