# Approximation Algorithms for the A Priori TravelingRepairman

## TL;DR

This paper introduces the first constant-factor approximation algorithm for the a priori traveling repairman problem with non-uniform probabilities, advancing the understanding of stochastic routing problems.

## Contribution

It provides the first constant-factor approximation algorithm for the a priori TRP with non-uniform probabilities, extending previous results limited to uniform probabilities.

## Key findings

- First constant-factor approximation for non-uniform probabilities in a priori TRP.
- Algorithm effectively minimizes expected arrival times in stochastic routing.
- Advances theoretical understanding of stochastic traveling repairman problems.

## Abstract

We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem (also called the traveling deliveryman or minimum latency problem). Given a metric $(V,d)$ with a root $r\in V$, the traveling repairman problem (TRP) involves finding a tour originating from $r$ that minimizes the sum of arrival-times at all vertices. In its a priori version, we are also given independent probabilities of each vertex being active. We want to find a master tour $\tau$ originating from $r$ and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when $\tau$ is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under non-uniform probabilities. Previously, such a result was only known for uniform probabilities.