The.Algorithm.Design.Manual.Springer-Verlag.1998

Graph Partition
annealing, is almost certain to be a good idea.
Implementations: Jon Berry's implementations of several graph partitioning heuristics, including
Kernighan-Lin, simulated annealing, and path optimization are available from
http://www.elon.edu/users/f/berryj/www/.
A non-network-flow-based implementation of minimum cut is included with LEDA (see Section ).
Notes: The fundamental heuristic for graph partitioning is due to Kernighan and Lin [KL70]. Empirical
results on graph partitioning heuristics include [BG95, LR93].
The planar separator theorem and an efficient algorithm for finding such a separator are due to Lipton
and Tarjan [LT79, LT80]. Although network flow can be used to find minimum cut sets in graphs, faster
algorithms are available, including [SW94] and [Kar96a].
Expositions on the hardness of max-cut [Kar72] include [Eve79a]. Note that any random vertex partition
will expect to cut half of the edges in the graph, since the probability that the two vertices defining an
edge end up on different sides of the partition is 1/2. Goemans and Williamson [GW95] gave an 0.878factor
approximation algorithm for maximum-cut, based on semidefinite programming techniques.
Tighter analysis of this algorithm followed by Karloff [Kar96b].
Related Problems: Edge/vertex connectivity (see page ), network flow (see page ).
Next: Vertex Coloring Up: Graph Problems: Hard Problems Previous: Hamiltonian Cycle
Algorithms
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