Natural disasters impact transportation networks adversely and cause road sections to be damaged or blocked. The road network may even become disconnected, impeding accessibility between disaster-stricken areas and critical locations such as hospitals, relief aid depots and transportation hubs. In the immediate response phase, a set of blocked edges should be selected and restored to reconnect the transportation network. While locations of the disrupted roads can be identified using drone or satellite images, an accurate estimation of time to restore a road segment can be carried out only after expert observations on the field. In this article, we study a post-disaster road restoration problem modeled on an undirected edge-weighted graph with $k$ blocked edges, where the unblocking time of a blocked edge is revealed online once the road restoration team visits an end-node of that blocked edge. The objective is to minimize the time at which the road network is reconnected. We first investigate the worst-case performance of online algorithms against offline optimal solutions by means of the competitive ratio. We prove that any online deterministic algorithm cannot achieve a competitive ratio better than $2k-1$. We also provide an optimal online algorithm that is proven to achieve this lower bound. In addition, to achieve good performance on realistic instances, we implement an algorithm that solves a mixed integer programming model each time new information is revealed. Since model solution is prohibitively time-consuming, we also propose a novel polynomial time online algorithm. We compare these two algorithms with two other benchmark online algorithms on both Istanbul road network instances and several other city instances from the literature. Our experiments show that the proposed polynomial time online algorithm performs superior to the benchmark ones and obtains solutions close to the offline optimum on all the tested instances.

自然灾害对交通网络产生不利影响，导致路段受损或堵塞。道路网络甚至可能会断开连接，从而阻碍受灾地区与医院、救济站和交通枢纽等关键地点之间的可达性。在即时响应阶段，应选择并恢复一组阻塞的边以重新连接交通网络。虽然可以使用无人机或卫星图像识别被破坏道路的位置，但只有在专家实地观察后才能准确估计恢复路段的时间。在本文中，我们研究了一个以无向边加权图为模型的灾后道路恢复问题，其中$克$阻塞边缘，一旦道路修复团队访问该阻塞边缘的终端节点，就会在线显示阻塞边缘的解锁时间。目标是最小化道路网络重新连接的时间。我们首先通过竞争比率研究在线算法相对于离线最优解的最坏情况性能。我们证明了任何在线确定性算法都无法达到比$2克-1$. 我们还提供了一种最佳在线算法，该算法已被证明可以实现此下限。此外，为了在现实实例上获得良好的性能，我们实现了一种算法，每次新信息出现时，该算法都会求解混合整数规划模型。由于模型求解非常耗时，我们还提出了一种新颖的多项式时间在线算法。我们在伊斯坦布尔道路网络实例和文献中的其他几个城市实例上将这两种算法与其他两种基准在线算法进行了比较。我们的实验表明，所提出的多项式时间在线算法的性能优于基准算法，并在所有测试实例上获得接近离线最优解的解。