In this paper, we address the problem of online car-sharing with variable booking times (CSV for short). In this scenario, customers submit ride requests, each specifying two important time parameters: the booking time and the pick-up time (start time), as well as two location parameters—the pick-up location and the drop-off location within a graph. For each request, it’s important to note that it must be booked before its scheduled start time. The booking time can fall within a specific interval prior to the request’s starting time. Additionally, each car is capable of serving only one request at any given time. The primary objective of the scheduler is to optimize the utilization of k cars to serve as many requests as possible. As requests arrive at their booking times, the scheduler faces an immediate decision: whether to accept or decline the request. This decision must be made promptly upon request submission, precisely at the booking time. We prove that no deterministic online algorithm can achieve a competitive ratio smaller than \(L+1\) even on a special case of a path (where L denotes the ratio between the largest and the smallest request travel time). For general graphs, we give a Greedy Algorithm that achieves \((3L+1)\)-competitive ratio for CSV. We also give a Parted Greedy Algorithm with competitive ratio \((\frac{5}{2}L+10)\) when the number of cars k is no less than \(\frac{5}{4}L+20\); for CSV on a special case of a path, the competitive ratio of Parted Greedy Algorithm is \((2L+10)\) when \(k\ge L+20\).

在本文中，我们解决了可变预订时间的在线汽车共享（简称 CSV）问题。在该场景中，客户提交乘车请求，每个请求指定两个重要的时间参数：预订时间和接载时间（开始时间），以及两个位置参数——某个范围内的上车地点和下车地点。图形。对于每个请求，请务必注意，必须在预定开始时间之前进行预订。预订时间可以落在请求开始时间之前的特定间隔内。此外，每辆车在任何给定时间只能满足一个请求。调度程序的主要目标是优化k辆汽车的利用率，以满足尽可能多的请求。当请求到达预订时间时，调度程序面临立即决定：是接受还是拒绝请求。该决定必须在提交请求后立即做出，且恰好是在预订时间。我们证明，即使在路径的特殊情况下（其中L表示最大和最小请求行程时间之间的比率），没有确定性在线算法可以实现小于\(L+1\)的竞争比。对于一般图，我们给出了一个贪心算法，可以实现CSV 的\((3L+1)\)竞争比。当汽车数量k不小于\(\frac{5}{4}L+20 ) 时，我们还给出了竞争比\((\frac{5}{2}L+10)\)的分部贪婪算法\) ;对于路径特殊情况下的 CSV，当\(k\ge L+20\)时，Parted Greedy 算法的竞争比为\((2L+10)\)。