A Primal Dual Algorithm for a Heterogeneous Traveling Salesman Problem

TL;DR

This paper introduces a primal-dual algorithm for a two-vehicle heterogeneous routing problem in surveillance, achieving a 2-approximation ratio to optimize target coverage with minimal total travel distance.

Contribution

The paper presents a novel primal-dual algorithm specifically designed for a two-vehicle heterogeneous routing problem with proven approximation guarantees.

Findings

Algorithm achieves a 2-approximation ratio.

Addresses routing with heterogeneous vehicles and multiple targets.

Provides a new approach for surveillance routing problems.

Abstract

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. In this article, we consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we consider a routing problem where there are two heterogeneous vehicles that start from distinct initial locations, and a set of targets. The objective is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances traveled by the vehicles is a minimum. We present a primal-dual algorithm for a variant of this routing problem that provides an approximation ratio of 2.