A General backtrack algorithm for the isomorphism problem of combinatorial objects
Journal of Symbolic Computation
A Fast Algorithm for Testing Isomorphism of Permutation Networks
IEEE Transactions on Computers
A randomized parallel algorithm for planar graph isomorphism
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Using graph distance in object recognition
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
Graph Isomorphism and Identification Matrices: Parallel Algorithms
IEEE Transactions on Parallel and Distributed Systems
A Fast Backtracking Algorithm to Test Directed Graphs for Isomorphism Using Distance Matrices
Journal of the ACM (JACM)
A Linear Time Algorithm for Deciding Interval Graph Isomorphism
Journal of the ACM (JACM)
Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs
Journal of the ACM (JACM)
Isomorphism testing for embeddable graphs through definability
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Correspondence and translation for heterogeneous data
Theoretical Computer Science
A general strategy for decomposing topological invariants of spatial databases and an application
Data & Knowledge Engineering
Topological Invariants for Lines
IEEE Transactions on Knowledge and Data Engineering
A Shape Analysis Model with Applications to a Character Recognition System
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient extraction of mapping rules of atoms from enzymatic reaction data
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Efficient Generation of Plane Triangulations without Repetitions
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Finding Planar Geometric Automorphisms in Planar Graphs
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Counting Graph Isomorphisms among Chordal Graphs with Restricted Clique Number
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Efficient Generation of Triconnected Plane Triangulations
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
European Journal of Combinatorics
A large database of graphs and its use for benchmarking graph isomorphism algorithms
Pattern Recognition Letters - Special issue: Graph-based representations in pattern recognition
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth 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
Testing isomorphism of cone graphs(Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Efficient generation of triconnected plane triangulations
Computational Geometry: Theory and Applications
Survey on structure-based case retrieval
The Knowledge Engineering Review
Graph Matching: A Fast Algorithm and Its Evaluation
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Frequent subgraph mining in outerplanar graphs
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
GPLAG: detection of software plagiarism by program dependence graph analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Compatible topologies on graphs: an application to graph isomorphism problem complexity
Theoretical Computer Science
Enumerating consistent metaquery instantiations
AI Communications
Computational properties of argument systems satisfying graph-theoretic constraints
Artificial Intelligence
IEEE Transactions on Computers
Generating unlabeled connected cubic planar graphs uniformly at random
Random Structures & Algorithms
Indexing through laplacian spectra
Computer Vision and Image Understanding
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Journal of Experimental Algorithmics (JEA)
Recursive Generation of 5-Regular Planar Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
Approximate graph edit distance computation by means of bipartite graph matching
Image and Vision Computing
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Efficient Suboptimal Graph Isomorphism
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Behavior based software theft detection
Proceedings of the 16th ACM conference on Computer and communications security
The complexity of the Hajós calculus for planar graphs
Theoretical Computer Science
Complete enumeration of compact structural motifs in proteins
ISB '10 Proceedings of the International Symposium on Biocomputing
Motorcycle graphs: canonical quad mesh partitioning
SGP '08 Proceedings of the Symposium on Geometry Processing
On graphs with unique node labels
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
Graph-based tools for data mining and machine learning
MLDM'03 Proceedings of the 3rd international conference on Machine learning and data mining in pattern recognition
Federation and sharing in the context marketplace
LoCA'07 Proceedings of the 3rd international conference on Location-and context-awareness
Frequent subgraph mining in outerplanar graphs
Data Mining and Knowledge Discovery
Object recognition through topo-geometric shape models using error-tolerant subgraph isomorphisms
IEEE Transactions on Image Processing
Constant time generation of biconnected rooted plane graphs
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Listing triconnected rooted plane graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Complexity classes of equivalence problems revisited
Information and Computation
From polynomial time queries to graph structure theory
Communications of the ACM
Deciding the isomorphism problem in classes of unary automatic structures
Theoretical Computer Science
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Identifying refactoring opportunities in process model repositories
Information and Software Technology
Physically-motivated dynamical algorithms for the graph isomorphism problem
Quantum Information & Computation
Proceedings of the 44th Annual Simulation Symposium
Fast suboptimal algorithms for the computation of graph edit distance
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Sampling unlabeled biconnected planar graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A linear time algorithm for constructing maximally symmetric straight-line drawings of planar graphs
GD'04 Proceedings of the 12th international conference on Graph Drawing
Reactive tabu search for measuring graph similarity
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Generating internally triconnected rooted plane graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Isomorphism for graphs of bounded feedback vertex set number
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Maximal words in sequence comparisons based on subword composition
Algorithms and Applications
A weight regularized relaxation based graph matching algorithm
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Multi-stage design for quasipolynomial-time isomorphism testing of steiner 2-systems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A quasi-polynomial time partition oracle for graphs with an excluded minor
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The Graph Isomorphism Problem and approximate categories
Journal of Symbolic Computation
Faster reaction mapping through improved naming techniques
Journal of Experimental Algorithmics (JEA)
Implementation of a solution to the conjugacy problem in Thompson's group F
ACM Communications in Computer Algebra
| Hi-index | 0.03 |
The isomorphism problem for graphs G1 and G2 is to determine if there exists a one-to-one mapping of the vertices of G1 onto the vertices of G2 such that two vertices of G1 are adjacent if and only if their images in G2 are adjacent. In addition to determining the existence of such an isomorphism, it is useful to be able to produce an isomorphism-inducing mapping in the case where one exists. The isomorphism problem for triconnected planar graphs is particularly simple since a triconnected planar graph has a unique embedding on a sphere [6]. Weinberg [5] exploited this fact in developing an algorithm for testing isomorphism of triconnected planar graphs in O(|V|2) time where V is the set consisting of the vertices of both graphs. The result has been extended to arbitrary planar graphs and improved to O(|V|log|V|) steps by Hopcroft and Tarjan [2,3]. In this paper, the time bound for planar graph isomorphism is improved to O(|V|). In addition to determining the isomorphism of two planar graphs, the algorithm can be easily extended to partition a set of planar graphs into equivalence classes of isomorphic graphs in time linear in the total number of vertices in all graphs in the set. A random access model of computation (see Cook [1]) is assumed. Although the proposed algorithm has a linear asymptotic growth rate, at the present stage of development it appears to be inefficient on account of a rather large constant. This paper is intended only to establish the existence of a linear algorithm which subsequent work might make truly efficient.