Online Ridesharing with Meeting Points [Technical Report]

TL;DR

This paper introduces the Meeting-Point-based Online Ridesharing Problem (MORP), proves its computational complexity, and proposes algorithms leveraging meeting points and $k$-skip covers to improve ridesharing efficiency.

Contribution

It formally defines MORP, proves its NP-hardness, and develops a hierarchical graph and algorithms utilizing meeting points and $k$-skip covers for better ridesharing solutions.

Findings

Algorithms outperform baseline methods in efficiency.

Meeting points increase rider service rates.

Proposed methods are validated on real and synthetic data.

Abstract

Nowadays, ridesharing becomes a popular commuting mode. Dynamically arriving riders post their origins and destinations, then the platform assigns drivers to serve them. In ridesharing, different groups of riders can be served by one driver if their trips can share common routes. Recently, many ridesharing companies (e.g., Didi and Uber) further propose a new mode, namely "ridesharing with meeting points". Specifically, with a short walking distance but less payment, riders can be picked up and dropped off around their origins and destinations, respectively. In addition, meeting points enables more flexible routing for drivers, which can potentially improve the global profit of the system. In this paper, we first formally define the Meeting-Point-based Online Ridesharing Problem (MORP). We prove that MORP is NP-hard and there is no polynomial-time deterministic algorithm with a constant competitive ratio for it. We notice that a structure of vertex set, $k$-skip cover, fits well to the MORP. $k$-skip cover tends to find the vertices (meeting points) that are convenient for riders and drivers to come and go. With meeting points, MORP tends to serve more riders with these convenient vertices. Based on the idea, we introduce a convenience-based meeting point candidates selection algorithm. We further propose a hierarchical meeting-point oriented graph (HMPO graph), which ranks vertices for assignment effectiveness and constructs $k$-skip cover to accelerate the whole assignment process. Finally, we utilize the merits of $k$-skip cover points for ridesharing and propose a novel algorithm, namely SMDB, to solve MORP. Extensive experiments on real and synthetic datasets validate the effectiveness and efficiency of our algorithms.