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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
The Optimal Route and Stops for a Group of Users in a Roa...
Radi Muhammad Reza, Mohammed Eunus Ali, Muhammad Aamir Cheema · 2017-06-24 · via cs.DS updates on arXiv.org

Recently, with the advancement of the GPS-enabled cellular technologies, the location-based services (LBS) have gained in popularity. Nowadays, an increasingly larger number of map-based applications enable users to ask a wider variety of queries. Researchers have studied the ride-sharing, the carpooling, the vehicle routing, and the collective travel planning problems extensively in recent years. Collective traveling has the benefit of being environment-friendly by reducing the global travel cost, the greenhouse gas emission, and the energy consumption. In this paper, we introduce several optimization problems to recommend a suitable route and stops of a vehicle, in a road network, for a group of users intending to travel collectively. The goal of each problem is to minimize the aggregate cost of the individual travelers' paths and the shared route under various constraints. First, we formulate the problem of determining the optimal pair of end-stops, given a set of queries that originate and terminate near the two prospective end regions. We outline a baseline polynomial-time algorithm and propose a new faster solution - both calculating an exact answer. In our approach, we utilize the path-coherence property of road networks to develop an efficient algorithm. Second, we define the problem of calculating the optimal route and intermediate stops of a vehicle that picks up and drops off passengers en-route, given its start and end stoppages, and a set of path queries from users. We outline an exact solution of both time and space complexities exponential in the number of queries. Then, we propose a novel polynomial-time-and-space heuristic algorithm that performs reasonably well in practice. We also analyze several variants of this problem under different constraints. Last, we perform extensive experiments that demonstrate the efficiency and accuracy of our algorithms.