单通道通道图上路由调度的加速算法
Speeding up Routing Schedules on Aisle-Graphs with Single Access
摘要：
在本文中，我们研究定向运动通道图单通道问题（OASP），一个变种的定向运动问题的机器人在一个所谓的单通道通道图，即，由一组只能从一侧访问的行组成的图。通道图模型，其中包括葡萄园或仓库。每个通道图顶点都与机器人访问顶点时获得的奖励相关联。由于机器人的能量是有限的，只有一个顶点的子集可以访问一个充满电的电池。我们的目标是最大化的总奖励收集的机器人与电池充电。首先，我们提出了一个最优算法，解决了OASP在O（m^2 n^2）时间的通道图与一个单一的访问组成的m行，每个n个顶点。以设计更快的解决方案为目标，我们提出了四个贪婪的次优算法，运行在最多O（mn（m+n））的时间。对于其中的两个，我们保证近似比为1/2（1-1/e），其中e是自然对数的底，通过利用众所周知的子模块属性的总回报。实验表明，这些算法收集超过80%的最佳奖励。
英文摘要：
In this paper, we study the Orienteering Aisle-graphs Single-access Problem (OASP), a variant of the orienteering problem for a robot moving in a so-called single-access aisle-graph, i.e., a graph consisting of a set of rows that can be accessed from one side only. Aisle-graphs model, among others, vineyards or warehouses. Each aisle-graph vertex is associated with a reward that a robot obtains when visits the vertex itself. As the robot's energy is limited, only a subset of vertices can be visited with a fully charged battery. The objective is to maximize the total reward collected by the robot with a battery charge. We first propose an optimal algorithm that solves OASP in O(m^2 n^2) time for aisle-graphs with a single access consisting of m rows, each with n vertices. With the goal of designing faster solutions, we propose four greedy sub-optimal algorithms that run in at most O(mn (m+n)) time. For two of them, we guarantee an approximation ratio of 1/2(1-1/e), where e is the base of the natural logarithm, on the total reward by exploiting the well-known submodularity property. Experimentally, we show that these algorithms collect more than 80% of the optimal reward.
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