A separator theorem for graphs of bounded genus
Journal of Algorithms
A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Topological graph theory
The graph genus problem is NP-complete
Journal of Algorithms
Pfaffian orientations 0-1 permanents, and even cycles in directed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Subgraph isomorphism in planar graphs and related problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A deterministic near-linear time algorithm for finding minimum cuts in planar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Biometric cryptosystem based on discretized fingerprint texture descriptors
Expert Systems with Applications: An International Journal
A comparative study of parallel algorithms for the girth problem
AusPDC '12 Proceedings of the Tenth Australasian Symposium on Parallel and Distributed Computing - Volume 127
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The girth of a graph G is the length of a shortest cycle of G. In this article we design an O(n5/4 log n) algorithm for finding the girth of an undirected n-vertex planar graph, the first o(n2) algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.