Meeting at the Border of Two Separate Domains

Abstract

To transmit information or transfer an object, two agents may need to reach the same location and meet. Often, such two agents operate in two separate environments and they can only meet at border locations. For example, a ship, sailing in the sea, needs to meet a truck traveling on land. These two agents are able to meet only at the shoreline. We call this problem the Meeting at the Border problem (MATB). In MATB, the optimal meeting location at the border is required, where the cost of a meeting location is the sum of the two shortest paths to that location. We show how to optimally solve MATB with heuristic search and suggest a novel heuristic function that estimates the cost of meeting at the border. Indeed, our new heuristic significantly enhances search algorithms in 2D and 3D domains.