A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph
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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.
KeywordsPrincipal sequence of partitions Network attack Network strength Minimum cut/maximum flow Parametric algorithm
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- 2.Narayanan, H.: The principal lattice of partitions of a submodular function. In: Linear Algebra and Its Applications, vol. 144, pp. 179–216 (1991) Google Scholar
- 10.Patkar, S., Narayanan, H.: Principal lattice of partitions of submodular functions on graphs: fast algorithms for principal partition and generic rigidity. In: Proc. of the 3rd Ann. Int. Symp. on Algorithms and Computation (ISAAC), Lecture Notes in Computer Science, vol. 650, pp. 41–50. Springer, Berlin (1992) Google Scholar
- 15.Edmonds, J.: Submodular functions, matroids and certain polyhedra. In: Proc. Calgary Int. Conf. on Combinatorial Structures and Applications, pp. 69–87 (1970) Google Scholar