The minimum broadcast time problem for several processor networks
Theoretical Computer Science
Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs
Journal of the ACM (JACM)
Marked Subgraph Isomorphism of Ordered Graphs
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
A large database of graphs and its use for benchmarking graph isomorphism algorithms
Pattern Recognition Letters - Special issue: Graph-based representations in pattern recognition
IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A Polynomial Algorithm for Submap Isomorphism
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Filtering for subgraph isomorphism
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Extracting plane graphs from images
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Polynomial algorithms for subisomorphism of nD open combinatorial maps
Computer Vision and Image Understanding
| Hi-index | 5.23 |
Graphs are used as models in a variety of situations. In some cases, e.g. to model images or maps, the graphs will be drawn in the plane, and this feature can be used to obtain new algorithmic results. In this work, we introduce a special class of graphs, called open plane graphs, which can be used to represent images or maps for robots: they are planar graphs embedded in the plane, in which certain faces can be removed, are absent or unreachable. We give a normal form for such graphs and prove that one can check in polynomial time if two normalised graphs are isomorphic, or if two open plane graphs are equivalent (their normal forms are isomorphic). Then we consider a new kind of subgraphs, built from subsets of faces and called patterns. We show that searching for a pattern in an open plane graph is tractable if and only if the faces are contiguous, that is, we prove that the problem is NP-complete otherwise.