An Efficient Insertion Operator in Dynamic Ridesharing Services

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 "insertion operator". 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 \rev{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 $O(n^3)$ , where $n$ 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 $O(n^2)$ . We further improve the time efficiency of the insertion operator to $O(n)$ 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.