Algorithmic Analysis for Ridesharing of Personal Vehicles

The ridesharing problem is to share personal vehicles by individuals (participants) with similar itineraries. A trip in the ridesharing problem is a participant and his/her itinerary. To realize a trip is to deliver the participant to his/her destination by a vehicle satisfying the itinerary requirement. We study two optimization problems in ridesharing: minimize the number of vehicles and minimize the total travel distance of vehicles to realize all trips. The minimization problems are complex and NP-hard because of many parameters. We simplify the problems by considering only the source, destination, vehicle capacity, detour distance and preferred path parameters. We prove that the simplified minimization problems are still NP-hard while a further simplified variant is polynomial time solvable. These suggest a boundary between the NP-hard and polynomial time solvable cases.