A separator theorem for graphs of bounded genus
Journal of Algorithms
The analysis of a nested dissection algorithm
Numerische Mathematik
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Planar separators and parallel polygon triangulation (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
Area-Efficient VLSI Computation
Area-Efficient VLSI Computation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
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We propose an algorithm for maintaining a partition of dynamic planar graphs motivated by applications in load balancing for solving partial differential equations on a shared memory multiprocessor. We consider planar graphs of bounded face sizes that can be modified by local insertions or deletions of vertices or edges so that planarity is preserved. In our paper we describe a data structure that can be updated in O(log n) time after any such modification of the graph, where n is the current size of the graph, and allows an almost optimal partition of a required size to be maintained. More precisely, the size of the separator is within an O(nδ) factor of the optimal for the class of planar graphs, where δ is any positive constant, and can be listed in time proportional to its size. The dynamic data structure occupies O(n) space and can initially be constructed in time linear to the size of the original graph.