A 1.5-Approximation Route Finding for a Ride-sharing considering Movement of Passengers

MaaS (stands for Mobility as a Service) is a concept that aims to integrate different transportation services into a unified and seamless mobility solution. It encourages a shift away from personally owned modes of transportation, such as private cars, towards a more comprehensive approach that combines public transportation, such as ride-sharing, bike-sharing, carpooling, and other modes of transport into a single and user-centric service. One of the services offered within MaaS is a ride-sharing, which provides several advantages such as cost savings, reduced traffic congestion, or environmental benefits. However, to make a ride-sharing efficient, a sophisticated route finding (i.e., planning) is required to avoid redundantly long routes when picking up or dropping off passengers.

In this paper, we consider an efficient ride-sharing route finding for large-vehicles such as buses that starts at the determined location and returns after visiting all the locations, when a set of the locations of the passengers is given. Moreover, we allow passengers to move within a short distance to find more efficient traversal plan. Note that this problem can be reduced to the traveling salesperson problem (with some constraints) which is a well-known NP-hard problem. Hence, we employ a 1.5-approximation algorithm to find an efficient route within a reasonable computational time, moreover, use the Viterbi algorithm to improve the efficiency of the route when allowing each passenger to move.