 
Summary: The (K, k)Capacitated Spanning Tree Problem
Esther M. Arkin
, Nili GuttmannBeck
, and Refael Hassin
No Institute Given
Abstract. This paper considers a generalization of the capacitated span
ning tree, in which some of the nodes have capacity K, and the others
have capacity k < K. We prove that the problem can be approximated
within a constant factor, and present better approximations when k is 1
or 2.
1 Introduction
Let G = (V, E) be an undirected graph with nonnegative edge weights l(e) e E
satisfying the triangle inequality. Let 1 k K be given integer capacities.
Assume that V = {r} VK Vk, where r is a root node, and VK and Vk are the
sets of nodes having capacity K and k, respectively. In the (K, k) capacitated
spanning tree problem we want to compute a minimum weight tree rooted
at r such that for each v V \{r} the number of nodes in the subtree rooted at
v is no bigger than its capacity.
We are motivated by the following: Nodes of the graph correspond to sensors
collecting data that must be transported to a given basestation, the root of the
