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Shared mobility is widely recognized for its contribution in reducing carbon footprint, traffic congestion, parking needs and transportation-related costs in urban and suburban areas. In this context, the use of carpooling in home-work commute is particularly appealing for its potential of lessening the number of cars and kilometers traveled, consequently reducing major causes of traffic in cities. Accord- ingly, most of the carpooling algorithms are optimized for reducing total travel time, cost, and other transportation-related metrics. In this paper, we analyze carpooling from a new perspective, investigating the question of whether it can be used also as a tool to favor social integration, and to what extent social benefits should be traded off with transportation efficiency. By incorporating traveler's social character- istics into a recently introduced network-based approach to model ride-sharing opportunities, we define two social-related carpooling problems: how to maximize the number of rides shared between people belonging to different social groups, and how to maximize the amount of time people spend together along the ride. For each of the problems, we provide corresponding optimal and computationally effi- cient solutions. We then demonstrate our approach on two datasets collected in the city of Pisa, Italy, and Cambridge, US, and quantify the potential social benefits of carpooling, and how they can be traded off with traditional transportation-related metrics. When collectively considered, the models, algorithms, and results presented in this paper broaden the perspective from which carpooling problems are typically analyzed to encompass multiple disciplines including urban planning, public policy, and social sciences.

Information and communication technologies have opened the way to new solutions for urban mobility that provide better ways to match individuals with on-demand vehicles. However, a fundamental unsolved problem is how best to size and operate a fleet of vehicles, given a certain demand for personal mobility. Previous studies(1-5) either do not provide a scalable solution or require changes in human attitudes towards mobility. Here we provide a network-based solution to the following 'minimum fleet problem', given a collection of trips (specified by origin, destination and start time), of how to determine the minimum number of vehicles needed to serve all the trips without incurring any delay to the passengers. By introducing the notion of a 'vehicle-sharing network', we present an optimal computationally efficient solution to the problem, as well as a nearly optimal solution amenable to real-time implementation. We test both solutions on a dataset of 150 million taxi trips taken in the city of New York over one year(6). The real-time implementation of the method with near-optimal service levels allows a 30 per cent reduction in fleet size compared to current taxi operation. Although constraints on driver availability and the existence of abnormal trip demands may lead to a relatively larger optimal value for the fleet size than that predicted here, the fleet size remains robust for a wide range of variations in historical trip demand. These predicted reductions in fleet size follow directly from a reorganization of taxi dispatching that could be implemented with a simple urban app; they do not assume ride sharing(7-9), nor require changes to regulations, business models, or human attitudes towards mobility to become effective. Our results could become even more relevant in the years ahead as fleets of networked, self-driving cars become commonplace(10-14).