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cs.DS updates on arXiv.org

PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Potential-Based Greedy Matching for Dynamic Delivery Pooling
Hongyao Ma, Will Ma, Matias Romero · 2025-02-24 · via cs.DS updates on arXiv.org

We study the dynamic pooling of multiple orders into a single trip, a strategy widely adopted by online delivery platforms. When an order has to be dispatched, the platform must determine which (if any) of the available orders to pool it with, weighing the immediate efficiency gains against the uncertain, differential benefits of holding each order for future pooling opportunities. In this paper, we demonstrate the effectiveness of using the delivery distance as a proxy for opportunity cost via a potential-based greedy algorithm (PB). The algorithm is simple, pooling each departing job with the available job that maximizes the immediate savings in travel distance minus "half its delivery distance", which we call the potential of the available job. Theoretically, we show that PB achieves vanishing worst-case regret per job as market density increases, whereas a naive greedy policy suffers constant regret. We further show that the potential approximates the true opportunity cost of dispatching a job, in a stochastic setting with sufficient density. Finally, we conduct extensive numerical experiments on both synthetic data and real-world data from the Meituan platform. Despite being forecast-agnostic, PB consistently outperforms greedy heuristics that rely on historical data. Moreover, PB achieves performance comparable to computationally-intensive batching heuristics, which themselves also benefit from incorporating the potential to further improve their performance or drastically reduce computational costs.