Speeding up Routing Schedules on Aisle Graphs With Single Access

In this article, we study the orienteering aisle-graph 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 it visits the vertex itself. As the energy of the robot 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 the OASP in <tex-math notation="LaTeX">O(m²n²)</tex-math> time for aisle graphs with a single access consisting of <tex-math notation="LaTeX">m</tex-math> rows, each with <tex-math notation="LaTeX">n</tex-math> vertices. With the goal of designing faster solutions, we propose four greedy suboptimal algorithms that run in at most <tex-math notation="LaTeX">O(mn\ (m + n))</tex-math> time. For two of them, we guarantee an approximation ratio of <tex-math notation="LaTeX">1/2(1 - 1/e)</tex-math> , where <tex-math notation="LaTeX">e</tex-math> 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.