FORM: Finding the Fair-Optimal Ridesharing Matching on Road Networks

Fairness in ridesharing attracts much attention from academia and industry in recent years. One of the typical definitions of fairness among passengers comes from the stable matching problem. Some studies employing this concept apply existing Basic Roommates Algorithm (BRA) to randomly yield a fair matching or fail to find one. In this paper, we aim to find the optimal fair matching that satisfied by the most passengers. Specifically, we propose the fair-optimal ridesharing matching (FORM) problem, and prove its np-hardness by the reduction from optimal roommates problem. To tackle FORM, we propose two methods, namely Worst Passenger Selection (WPS) and Minimum Cost Selection (MCS), based on the key operation of BRA. We prove the approximation ratio of WPS is $\frac{4}{7}$ . Besides, we devise GFRM method to handle unsolvable case to guarantee a fair solution. Finally, we extend our solution framework to a more general scenario where more than two passengers sharing a ride together. Through extensive experiments, we demonstrate the efficiency and effectiveness of our proposed approaches on New York City taxi trip data set. In summary, our framework improves the total cost saving of passengers by 9% $\sim 15\%$ (compared with BRA) and the platform revenue by 17% (compared with the state-of-the-art passenger matching algorithm GAS) with a guarantee of the fairness among passengers.