A linear-time algorithm for finding an edge-partition with max-min ratio at most two

Authors:
An-Chiang Chu;Bang Ye Wu;Kun-Mao Chao
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 106, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Min-Hsiung, Chiayi, 621, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 106, Taiwan and Graduate Institute of Biomedical Electronics and Bioinformatics, National Taiwan Uni ...
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

Given a positive integer k and an undirected edge-weighted connected simple graph G with at least k edges of positive weight, we wish to partition the graph into k edge-disjoint connected components of approximately the same size. We focus on the max-min ratio of the partition, which is the weight of the maximum component divided by that of the minimum component. It has been shown that for some instances, the max-min ratio is at least two. In this paper, for any graph with no edge weight larger than one half of the average weight, we provide a linear-time algorithm for delivering a partition with max-min ratio at most two. Furthermore, by an extreme example, we show that the above restriction on edge weights is the loosest possible.