Non-Exclusive Notifications for Ride-Hailing at Lyft I: Single-Cycle Approximation Algorithms

A research team from Lyft and academia has published the first part of a two-part study, introducing novel algorithms to solve a core inefficiency in ride-hailing: the 'Notification Set Selection Problem.' When a ride request comes in, the platform must decide which subset of drivers to notify simultaneously. The paper formally models this as a combinatorial optimization problem under two real-world protocols: 'First Acceptance' (FA) for speed and 'Best Acceptance' (BA) for match quality. The team proved that maximizing welfare under both is strongly NP-hard, meaning no perfectly efficient solution exists for all cases.

Despite this complexity, the researchers derived several practical algorithmic breakthroughs. For the FA protocol, they developed a Polynomial Time Approximation Scheme (PTAS) for single-rider cases and a constant 4-factor approximation for general matching. For the BA protocol, they proved the objective is monotone and submodular, allowing for a standard (1 - 1/e)-approximation. Crucially, they designed a polynomial-time demand oracle that can surpass this performance barrier. In a key simplification, they showed that with homogeneous driver acceptance probabilities, the BA problem can be solved exactly and efficiently using linear programming. The algorithms were validated on synthetic data and instances calibrated with real Lyft ride-sharing data, proving their practical utility for scaling real-time dispatch systems.