{"date_updated":"2021-01-12T07:41:46Z","page":"394 - 412","month":"04","volume":56,"date_created":"2018-12-11T12:01:59Z","publication":"Algorithmica","quality_controlled":0,"_id":"3202","title":"A faster algorithm for computing the principal sequence of partitions of a graph","author":[{"full_name":"Vladimir Kolmogorov","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"date_published":"2010-04-01T00:00:00Z","type":"journal_article","day":"01","year":"2010","status":"public","publication_status":"published","citation":{"chicago":"Kolmogorov, Vladimir. “A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph.” <i>Algorithmica</i>. Springer, 2010. <a href=\"https://doi.org/10.1007/s00453-008-9177-z\">https://doi.org/10.1007/s00453-008-9177-z</a>.","ieee":"V. Kolmogorov, “A faster algorithm for computing the principal sequence of partitions of a graph,” <i>Algorithmica</i>, vol. 56, no. 4. Springer, pp. 394–412, 2010.","ama":"Kolmogorov V. A faster algorithm for computing the principal sequence of partitions of a graph. <i>Algorithmica</i>. 2010;56(4):394-412. doi:<a href=\"https://doi.org/10.1007/s00453-008-9177-z\">10.1007/s00453-008-9177-z</a>","short":"V. Kolmogorov, Algorithmica 56 (2010) 394–412.","apa":"Kolmogorov, V. (2010). A faster algorithm for computing the principal sequence of partitions of a graph. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/s00453-008-9177-z\">https://doi.org/10.1007/s00453-008-9177-z</a>","ista":"Kolmogorov V. 2010. A faster algorithm for computing the principal sequence of partitions of a graph. Algorithmica. 56(4), 394–412.","mla":"Kolmogorov, Vladimir. “A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph.” <i>Algorithmica</i>, vol. 56, no. 4, Springer, 2010, pp. 394–412, doi:<a href=\"https://doi.org/10.1007/s00453-008-9177-z\">10.1007/s00453-008-9177-z</a>."},"doi":"10.1007/s00453-008-9177-z","intvolume":"        56","extern":1,"issue":"4","publist_id":"3480","abstract":[{"text":"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.","lang":"eng"}],"publisher":"Springer"}