Algorithmic analysis for ridesharing of personal vehicles

Abstract

The ridesharing problem is to share personal vehicles by individuals with similar itineraries. A trip in the ridesharing problem is an individual and his/her itinerary. To realize a trip is to deliver the individual to his/her destination by a vehicle satisfying the itinerary requirement. Major optimization goals in the ridesharing problem include minimizing the number of vehicles and minimizing the total travel distance of vehicles to realize all trips. There are many parameters in the minimization problems, making them complex and NP-hard. The problems can be simplified by considering only some of the parameters. We give an algorithmic analysis for the simplified minimization problems and explore a boundary between the NP-hard and polynomial time solvable cases. We prove that the simplified minimization problems, where only the source, destination, vehicle capacity, detour distance and preferred path parameters are considered, are still NP-hard. We show that the simplified problem of minimizing the number of vehicles becomes polynomial time solvable if the considered parameters satisfy certain conditions. These suggest a boundary between the NP-hard and polynomial time solvable cases.