Approximation Algorithms for P2P Orienteering and Stochastic Vehicle Routing Problem

TL;DR

This paper introduces approximation algorithms for P2P orienteering and stochastic vehicle routing, providing near-optimal solutions for complex routing problems with uncertainty and constraints.

Contribution

It presents a (2+ε)-approximation algorithm for P2P orienteering on general metrics and extends to stochastic vehicle routing with time-windows.

Findings

Achieved a (2+ε)-approximation for P2P orienteering.

Developed a constant-factor approximation for stochastic vehicle routing.

Extended the approach to handle stochastic rewards and time constraints.

Abstract

We consider the P2P orienteering problem on general metrics and present a (2+{\epsilon}) approximation algorithm. In the stochastic P2P orienteering problem we are given a metric and each node has a fixed reward and random size. The goal is to devise a strategy for visiting the nodes so as to maximize the expected value of the reward without violating the budget constraints. We present an approximation algorithm for the non-adaptive variant of the P2P Stochastic orienteering. As an implication of the approximation to the stochastic P2P orienteering problem, we define a stochastic vehicle routing problem with time-windows and present a constant factor approximation solution.