How Many Passengers Can We Serve with Ride-sharing?

Ride-sharing can reduce traffic congestion and thus reduce gas emissions and save travel time. However, transportation system with ride-sharing is currently inefficient due to low occupancy rate, high travel demand and some other factors. Existing literature did not consider ride-sharing with multi-request grouped in one trip. In our paper, we firstly proposed a graph-based algorithm that can obtain an approximation solution in polynomial time and then proposed an exact algorithm to solve this problem with maximizing the number of passenegers served in $O({1.2312}^{\mathrm{\mid }\mathcal{E}\mathrm{\mid }})$ time.