Skip to Main content Skip to Navigation
Journal articles

Approximation and inapproximability results on balanced connected partitions of graphs

Abstract : Let G=(V,E) be a connected graph with a weight function w: V \to \mathbbZ₊, and let q ≥q 2 be a positive integer. For X⊆ V, let w(X) denote the sum of the weights of the vertices in X. We consider the following problem on G: find a q-partition P=(V₁,V₂, \ldots, V_q) of V such that G[V_i] is connected (1≤q i≤q q) and P maximizes \rm min\w(V_i): 1≤q i≤q q\. This problem is called \textitMax Balanced Connected q-Partition and is denoted by BCP_q. We show that for q≥q 2 the problem BCP_q is NP-hard in the strong sense, even on q-connected graphs, and therefore does not admit a FPTAS, unless \rm P=\rm NP. We also show another inapproximability result for BCP₂ on arbitrary graphs. On q-connected graphs, for q=2 the best result is a \frac43-approximation algorithm obtained by Chleb\'ıková; for q=3 and q=4 we present 2-approximation algorithms. When q is not fixed (it is part of the instance), the corresponding problem is called \textitMax Balanced Connected Partition, and denoted as BCP. We show that BCP does not admit an approximation algorithm with ratio smaller than 6/5, unless \rm P=\rm NP.
Document type :
Journal articles
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Wednesday, March 26, 2014 - 4:59:23 PM
Last modification on : Tuesday, July 31, 2018 - 3:04:02 PM
Long-term archiving on: : Thursday, June 26, 2014 - 11:55:42 AM


Files produced by the author(s)




Frédéric Chataigner, Liliane R. B. Salgado, yoshiko Wakabayashi. Approximation and inapproximability results on balanced connected partitions of graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, Vol. 9 no. 1 (1), pp.177--192. ⟨10.46298/dmtcs.384⟩. ⟨hal-00966506⟩



Record views


Files downloads