An arc orienteering algorithm to find the most scenic path on a large-scale road network

Traditional route planning problems mainly focus on finding the shortest path considering the travel distance or time. In this paper, we aim to find the most scenic path that offers the most beautiful sceneries on the arcs of a path while the total travel cost (distance or time) is within a user-specified budget. This is a challenging problem as the optimization objective is to maximize the value of the path (i.e., its scenic value) instead of minimizing its cost (distance or time). The problem can be formulated as a variant of the Arc Orienteering Problem (AOP), which is a well-known NP-hard combinatorial optimization problem. Due to the fast response-time requirements of interactive mobile and online applications (e.g., within 300 milliseconds) and the large scale of real-world road networks, existing heuristic algorithms for AOP fail to solve the most scenic road problem. Therefore, unlike the existing approaches for AOP where they treat the road network as a traditional graph in which all-pair distances are pre-computed a priori, in this work, we treat the road network as a spatial network, utilizing the techniques from the field of spatial database: ellipse pruning and spatial indexing. Experiments on two real-world datasets demonstrate the efficiency and accuracy of our proposed algorithms, which can achieve over 95% accuracy within 300 milliseconds on large-scale datasets (over 100K network nodes).