Approximate ridesharing of personal vehicles problem

Abstract

It is important to find ride matches for individuals who participate in ridesharing quickly, and it is equally important to minimize the number of drivers to serve all individuals and minimize the total travel distance of the vehicles. This paper considers the following ridesharing problem: given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to their destinations while satisfying the requirements and achieving some optimization goal. Requirements of trips are specified by parameters including source, destination, vehicle capacity, preferred paths, detour distance and number of stops a driver is willing to make, and time constraints. We consider two optimization problems: minimizing the number of selected vehicles and minimizing total travel distance of the vehicles. We prove that it is NP-hard to approximate both minimization problems within a constant factor if any one of the requirements related to the detour distance, preferred paths, number of stops and time constraints is not satisfied. We give K+22-approximation algorithms for minimizing the number of selected vehicles when the requirement related to the number of stops is not satisfied, where K is the largest capacity of all vehicles.