Planar separators and parallel polygon triangulation
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Disk packings and planar separators
Proceedings of the twelfth annual symposium on Computational geometry
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
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Graph separators: a parameterized view
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Partitioning planar graphs with costs and weights
Journal of Experimental Algorithmics (JEA)
Engineering planar separator algorithms
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Structured recursive separator decompositions for planar graphs in linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider classical linear-time planar separator algorithms, determining for a given planar graph a small subset of its nodes whose removal divides the graph into two components of similar size. These algorithms are based on planar separator theorems, which guarantee separators of size O(&sqrt;n) and remaining components of size at most 2n/3 (where n denotes the number of nodes in the graph). In this article, we present a comprehensive experimental study of the classical algorithms applied to a large variety of graphs, where our main goal is to find separators that do not only satisfy upper bounds, but also possess other desirable characteristics with respect to separator size and component balance. We achieve this by investigating a number of specific alternatives for the concrete implementation and fine-tuning of certain parts of the classical algorithms. It is also shown that the choice of several parameters influences the separation quality considerably. Moreover, we propose as planar separators the usage of fundamental cycles, whose size is at most twice the diameter of the graph: For graphs of small diameter, the guaranteed bound is better than the O(&sqrt;n) bounds, and it turns out that this simple strategy almost always outperforms the other algorithms, even for graphs with large diameter.