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式通知——即同时向多名司机广播单一请求——以缓解司机接受意愿不确定所导致的效率低下问题。本文是Lyft合作的两部分研究中的第一部分，我们正式对单决策周期的“通知集合选择问题”进行建模，该问题中平台需为每个到来的乘车请求确定最优的司机通知子集。我们在两种竞争解决协议下分析这一组合优化问题：“首次接受（FA）”协议优先考虑速度，将订单分配给最先响应的司机；而“最优接受（BA）”协议则优先考虑匹配质量，选择价值最高的接受司机。我们证明，在这两种机制下最大化社会福利均为强NP难问题，排除了完全多项式时间近似方案（FPTAS）的存在性。尽管存在这一困难，我们仍推导出若干正面算法结果。针对FA协议，我们提出了单乘客情形下的多项式时间近似方案（PTAS）以及一般匹配场景中的常数因子近似（因子4）。我们强调FA估值函数可视为一种新颖的离散选择模型，其理论性质具有独立研究价值。针对BA协议，我们证明目标函数具有单调性和子模性，可达到标准的$(1 - 1/e)$近似比。此外，通过为这一问题设计的多项式时间需求预言机，我们证明能够突破$(1 - 1/e)$的近似比极限。最后，在均匀接受概率的特殊情形下，我们证明BA问题可通过线性规划公式在多项式时间内精确求解。我们通过合成数据及基于Lyft真实网约车数据标定的实例进行数值实验，验证了算法的实证性能。