Approximation and inapproximability results on balanced connected partitions of graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2007

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.
Fichier principal
Vignette du fichier
656-2516-1-PB.pdf (218.49 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00966506 , version 1 (26-03-2014)

Identifiers

Cite

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

Collections

TDS-MACS
146 View
1053 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More