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- W2013276661 abstract "Let G=(V,E) be a connected graph with a weight function w:V→Z+, and let 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,…,Vq) of V such that G[Vi] is connected (1≤i≤q) and P maximizes min{w(Vi):1≤i≤q}. This problem is called Max Balanced Connected q-Partition and is denoted by BCPq. We show that for q≥2 the problem BCPq is NP-hard in the strong sense, even on q-connected graphs. This result implies that this problem does not admit a FPTAS, unless P=NP. For these graphs, for q=2 the best result is a 43-approximation algorithm obtained by Chlebíková [J. Chlebíková. “Approximating the maximally balanced connected partition problem in graphs”, Information Processing Letters, 60:225–230, 1996]; for q=3 we present a 2-approximation algorithm. We also show a non-approximability result for BCP2." @default.
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- W2013276661 date "2004-12-01" @default.
- W2013276661 modified "2023-10-18" @default.
- W2013276661 title "Approximation Results on Balanced Connected Partitions of Graphs" @default.
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- W2013276661 doi "https://doi.org/10.1016/j.endm.2004.06.033" @default.
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