Locating Charging Stations: Connected, Capacitated and Prize- Collecting

TL;DR

This paper develops constant factor approximation algorithms for locating charging stations considering both connectivity and capacity constraints, extending to prize-collecting variants, thus addressing complex, combined constraints in facility location problems.

Contribution

It introduces the first constant factor approximations for combined connectivity and capacity constraints in facility location problems, including prize-collecting variants.

Findings

First constant factor approximations for combined constraints

Extension of techniques to prize-collecting variants

Addresses complex, combined constraints in facility location problems

Abstract

In this paper, we study locating charging station problem as facility location problem and its variants ($k$-Median, $k$-Facility location and $k$-center). We study the connectivity and the capacity constraints in these problem. Capacity and connectivity constraints have been studied in the literature separately for all these problems. We give first constant factor approximations when both the constraints are present. Extending/modifying the techniques used for connected variants of the problem to include capacities or for capacitated variants of problem to include connectivity is a tedious and challenging task. In this paper, we combine the two constraints by reducing the problem to underlying well studied problems, solving them as black box and combine the obtained solutions. We also, combine the two constraints in the prize-collection set up. In the prize-collecting set up, the problems are not even studied when one of the constraint is present. We present constant factor approximation for them as well.