In this paper, we make a first attempt to incorporate both commuting demand and transit network connectivity in bus route planning (CT-Bus), and formulate it as a constrained optimization problem: planning a new bus route with k edges over an existing transit network without building new bus stops to maximize a linear aggregation of commuting demand and connectivity of the transit network. We prove the NP-hardness of CT-Bus and propose an expansion-based greedy algorithm that iteratively scans potential candidate paths in the network. To boost the efficiency of computing the connectivity of new networks with candidate paths, we convert it to a matrix trace estimation problem and employ a Lanczos method to estimate the natural connectivity of the transit network with a guaranteed error bound. Furthermore, we derive upper bounds on the objective values and use them to greedily select candidates for expansion. Our experiments conducted on real-world transit networks in New York City and Chicago verify the efficiency, effectiveness, and scalability of our algorithms.
翻译:在本文中,我们首次尝试将通勤需求和过境网络连接纳入公共汽车路线规划(CT-Bus),并将其作为一个有限的优化问题:规划一个新的公共汽车路线,在现有过境网络上加上K边缘,而不建造新的公共汽车站,以最大限度地实现通勤需求和过境网络连接的线性汇总;我们证明CT-Bus的NP-硬性,并提议一个基于扩大的贪婪算法,对网络中的潜在候选路径进行迭接扫描;为了提高计算新网络连接和候选路径的效率,我们将其转换为矩阵跟踪估计问题,并使用兰克佐斯方法来估计过境网络的自然连接性,但有一定的错误。此外,我们从客观值中获取上限,并利用它们贪婪地选择扩展的候选者。我们在纽约市和芝加哥对真实世界过境网络进行的实验证实了我们算法的效率、有效性和可扩展性。