Solving the Watchman Route Problem on a Grid with Heuristic Search

Abstract

In this paper we optimally solve the Watchman Route Problem (WRP) on a grid. We are given a grid map with obstacles and the task is to (offline) find a (shortest) path through the grid such that all cells in the map can be visually seen by at least one cell on the path. We formalize WRP as a heuristic search problem and solve it with an A*-based algorithm. We develop a series of admissible heuristics with increasing difficulty and accuracy. In particular, our heuristics abstract the problem into line-of-sight clusters graph. Then, solutions for the minimum spanning tree (MST) and the traveling salesman problem (TSP) on this graph are used as admissible heuristics for WRP. We theoretically and experimentally study these heuristics and show that we can optimally and suboptimally solve problems of increasing difficulties.