A linear-time algorithm for finding an edge-partition with max-min ratio at most two
Journal
Discrete Applied Mathematics
Journal Volume
161
Journal Issue
7-8
Pages
932-943
Date Issued
2013
Author(s)
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. © 2012 Elsevier B.V. All rights reserved.
Type
journal article