Capacitated Domination: Constant Factor Approximation for Planar Graphs

TL;DR

This paper introduces a constant factor approximation algorithm for the capacitated domination problem on planar graphs, leveraging a novel hierarchical approach to improve solutions for capacitated covering problems.

Contribution

It presents the first constant factor approximation for capacitated domination on planar graphs using a new hierarchical perspective on outer-planar graph structures.

Findings

First constant factor approximation for planar graphs

New hierarchical approach for outer-planar graphs

Potential applicability to other capacitated covering problems

Abstract

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of each vertex is fully-assigned to some of its closed neighbours without exceeding the amount of capacity they provide. In this paper, we provide the first constant factor approximation for this problem on planar graphs, based on a new perspective on the hierarchical structure of outer-planar graphs. We believe that this new perspective and technique can be applied to other capacitated covering problems to help tackle vertices of large degrees.