An Efficient Insertion Operator in Dynamic Ridesharing Services
Yi Xu, Yongxin Tong, Yexuan Shi, Tao Qian, Ke Xu, Wei Li
Abstract
Dynamic ridesharing refers to services that arrange one-time shared rides on short notice. It underpins various real-world intelligent transportation applications such as car-pooling, food delivery and last-mile logistics. A core operation in dynamic ridesharing is the “ <i>insertion operator</i> ”. Given a worker and a feasible route which contains a sequence of origin-destination pairs from previous requests, the insertion operator inserts a new origin-destination pair from a newly arrived request into the current route such that certain objective is optimized. Common optimization objectives include minimizing the maximum/sum flow time of all requests and minimizing the total travel time of the worker. Despite its frequent usage, the insertion operator has a time complexity of <inline-formula><tex-math notation="LaTeX">$O(n^3)$</tex-math></inline-formula> , where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of all requests assigned to the worker. The cubic running time of insertion fundamentally limits the efficiency of urban-scale dynamic ridesharing based applications. In this paper, we propose a novel partition framework and a dynamic programming based insertion with a time complexity of <inline-formula><tex-math notation="LaTeX">$O(n^2)$</tex-math></inline-formula> . We further improve the time efficiency of the insertion operator to <inline-formula><tex-math notation="LaTeX">$O(n)$</tex-math></inline-formula> harnessing efficient index structures, such as fenwick tree. Evaluations on two real-world large-scale datasets show that our methods can accelerate insertion by 1.5 to 998.1 times.