Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Edge separators of planar and outerplanar graphs with applications
Journal of Algorithms
Massively parallel methods for engineering and science problems
Communications of the ACM
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Geometric Mesh Partitioning: Implementation and Experiments
SIAM Journal on Scientific Computing
Graph Separator Algorithms: A Refined Analysis
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Engineering planar separator algorithms
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Approximate shortest path queries on weighted polyhedral surfaces
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
I/O-Efficient algorithms on near-planar graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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A graph separator is a set of vertices or edges whose removal divides an input graph into components of bounded size. This paper describes new algorithms for computing separators in planar graphs as well as techniques that can be used to speed up their implementation and improve the partition quality. In particular, we consider planar graphs with costs and weights on the vertices, where weights are used to estimate the sizes of the components and costs are used to estimate the size of the separator. We show that one can find a small separator that divides the graph into components of bounded size. We describe implementations of the partitioning algorithms and discuss results of our experiments.