A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph
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- Kolmogorov, V. Algorithmica (2010) 56: 394. doi:10.1007/s00453-008-9177-z
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We consider the following problem: given an undirected weighted graph G=(V,E,c) with nonnegative weights, minimize function c(δ(Π))−λ|Π| for all values of parameter λ. Here Π is a partition of the set of nodes, the first term is the cost of edges whose endpoints belong to different components of the partition, and |Π| is the number of components. The current best known algorithm for this problem has complexity O(|V|2) maximum flow computations. We improve it to |V| parametric maximum flow computations. We observe that the complexity can be improved further for families of graphs which admit a good separator, e.g. for planar graphs.