Ride-hailing platforms increasingly rely on non-exclusive notifications-broadcasting a single request to multiple drivers simultaneously-to mitigate inefficiencies caused by uncertain driver acceptance. In this paper, the first in a two-part collaboration with Lyft, we formally model the 'Notification Set Selection Problem' for a single decision cycle, where the platform determines the optimal subset of drivers to notify for each incoming ride request. We analyze this combinatorial optimization problem under two contention-resolution protocols: 'First Acceptance (FA)', which prioritizes speed by assigning the ride to the first responder, and 'Best Acceptance (BA)', which prioritizes match quality by selecting the highest-valued accepting driver. We show that welfare maximization under both mechanisms is strongly NP-hard, ruling out a Fully Polynomial Time Approximation Scheme (FPTAS). Despite this, we derive several positive algorithmic results. For FA, we present a Polynomial Time Approximation Scheme (PTAS) for the single-rider case and a constant-factor approximation (factor 4) for the general matching setting. We highlight that the FA valuation function can be viewed as a novel discrete choice model with theoretical properties of independent interest. For BA, we prove that the objective is monotone and submodular, admitting a standard $(1 - 1/e)$-approximation. Moreover, using a polynomial-time demand oracle that we design for this problem, we show it is possible to surpass the $(1 - 1/e)$ barrier. Finally, in the special case of homogeneous acceptance probabilities, we show that the BA problem can be solved exactly in polynomial time via a linear programming formulation. We validate the empirical performance our algorithms through numerical experiments on synthetic data and on instances calibrated using real ride-sharing data from Lyft.

翻译：网约车平台日益依赖非独占通知机制——将单个请求同时广播给多位司机——以缓解因司机接受不确定性导致的效率损失。本文作为与Lyft两阶段合作研究的第一部分，首次对单决策周期的"通知集合选择问题"进行形式化建模，即平台需为每个新到达的乘车请求确定最优的司机通知子集。我们分析了两种竞争解决协议下的该组合优化问题："首次接受(FA)"优先考虑响应速度，将订单分配给最先应答的司机；"最优接受(BA)"则通过选择评分最高的接单司机来优化匹配质量。研究表明，两种机制下的福利最大化问题均属于强NP难问题，排除了完全多项式时间近似方案(FPTAS)的存在。尽管如此，我们仍获得了若干正向算法结果。对于FA机制，我们针对单乘客场景提出了多项式时间近似方案(PTAS)，并在一般匹配场景下给出了常数因子近似(因子4)。值得关注的是，FA估值函数可被解释为一种新型离散选择模型，其理论性质具有独立研究价值。对于BA机制，我们证明目标函数具有单调性和子模性，可实现标准$(1 - 1/e)$近似比。此外，通过为该问题设计的多项式时间需求预言机，我们证明可以突破$(1 - 1/e)$的近似瓶颈。最后，在司机接受概率同质的特殊情形下，我们展示可通过线性规划形式化在多项式时间内精确求解BA问题。我们利用合成数据及基于Lyft真实拼车数据校准的实例，通过数值实验验证了算法的实证性能。