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188宝金博页面版: A min-max relation in flowgraphs

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内容提示: A min-max relation in flowgraphsCarlos E. Ferreira1,2Institute of Mathematics and StatisticsUniversity of S? ao Paulo, S? ao Paulo, Brazil?Alvaro J. P. Franco1,2Ararangu? a CampusFederal University of Santa Catarina, Araranguá, BrazilAbstractWe have considered the problem of finding vertex-disjoint dipaths in flowgraphs andwe observed an interesting min-max relation: given a flowgraph G, the minimumsize of a dominator cover in G is equal to the maximum size of a junction partitionof G. In many optimiz...

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A min-max relation in flowgraphsCarlos E. Ferreira1,2Institute of Mathematics and StatisticsUniversity of S˜ ao Paulo, S˜ ao Paulo, Brazil´Alvaro J. P. Franco1,2Ararangu´ a CampusFederal University of Santa Catarina, Araranguá, BrazilAbstractWe have considered the problem of finding vertex-disjoint dipaths in flowgraphs andwe observed an interesting min-max relation: given a flowgraph G, the minimumsize of a dominator cover in G is equal to the maximum size of a junction partitionof G. In many optimization problems those relations are closely related to efficientalgorithms to solve them.Keywords: Flowgraphs, dominators, junctions, vertex-disjoint dipaths.1 IntroductionIn [2] we described an efficient algorithm that receives an acyclic digraph Dand a vertex s of D, and returns a partition B of the set of vertices of D suchthat, taking any pair of vertices {u,v}, u and v are in different parts of B if1Supported by CNPq Proc. 456792/2014-7 and FAPESP Proc. 2013/03447-62Emails: cef@ime.usp.br, alvaro.junio@ufsc.brAvailable online at www.sciencedirect.comElectronic Notes in Discrete Mathematics 50 (2015) 109–1141571-0653/© 2015 Elsevier B.V. All rights reserved.www.elsevier.com/locate/endmhttp://dx.doi.org/10.1016/j.endm.2015.07.019

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