Optimal traversal planning in road networks with navigational constraints

A frequent query in geospatial planning and decision making domains (e.g., emergency response, data acquisition, street cleaning), is to find an optimal traversal plan (OTP) that traverses an entire area (e.g., a city) by navigating through all its streets. The optimality is defined in terms of the time it takes to complete the traversal. This time depends on the number of times each street segment is traversed as well as the navigation time such as the time spent on changing direction at each intersection. While the problem roots in the classic problems of graph theory, real-world geospatial constraints of road network introduce new application-specific challenges. In this paper, we propose two algorithms to find OTP of a directed road network. Our greedy algorithm employs a classic graph traversal algorithm. During the traversal, it utilizes a set of heuristics at each intersection to minimize the total travel time. Our near-optimal algorithm, however, reduces an OTP problem to an Asymmetric Traveling Salesman Problem (ATSP) by extracting the dual graph of the original network in which each edge is represented by a graph node. Using an approximate solution for ATSP, our algorithm finds a near optimal answer. Our experiments using real-world road networks verify that our near-optimal algorithm outperforms the greedy algorithm in terms of the overall cost of its generated traversal by a factor of two, while its complexity is tolerable in real-world cases.