2020/09/25 by Marco Pavone, Pavone, Marco, Amin Saberi +5
Business, Management and Accounting · Computer Science · #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Optimization and Search Problems #Sharing Economy and Platforms
paper · pdf · doi:10.48550/arxiv.2009.12022
openalex publication_date 2020/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an online hypergraph matching problem with delays, motivated by ridesharing applications. In this model, users enter a marketplace sequentially, and are willing to wait up to d timesteps to be matched, after which they will leave the system in favor of an outside option. A platform can match groups of up to k users together, indicating that they will share a ride. Each group of users yields a match value depending on how compatible they are with one another. As an example, in ridesharing, k is the capacity of the service vehicles, and d is the amount of time a user is willing to wait for a driver to be matched to them. We present results for both the utility maximization and cost minimization variants of the problem. In the utility maximization setting, the optimal competitive ratio is (1)/(d) whenever k ≥ 3, and is achievable in polynomial-time for any fixed k. In the cost minimization variation, when k = 2, the optimal competitive ratio for deterministic algorithms is (3)/(2) and is achieved by a polynomial-time thresholding algorithm. When k>2, we show that a polynomial-time randomized batching algorithm is (2 - (1)/(d)) log k-competitive, and it is NP-hard to achieve a competitive ratio better than log k - O (log log k).