Generalized Watchman Route Problem with Discrete View Cost

In this paper, we introduce a generalized version of the Watchman Route Problem (WRP) where the objective is to plan a continuous closed route in a polygon (possibly with holes) and a set of discrete viewpoints on the planned route. Each planned viewpoint has some associated cost. The total cost to minimize is a weighted sum of the view cost, proportional to the number of viewpoints, and the travel cost, the total length of the route. We call this problem the Generalized Watchman Route Problem or the GWRP in short. We tackle a restricted nontrivial (it remains NP-hard and log-inapproximable) version of GWRP where each polygon edge is entirely visible from at least one planned viewpoint. We call it Whole Edge Covering GWRP. Our algorithm proposed first constructs a graph that connects O(n12 ) number of sample points in the polygon, where n is the number of polygon vertices; and then solves the corresponding View Planning Problem with Combined View and Traveling Cost, using an LP-relax...

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Pengpeng Wang, Ramesh Krishnamurti, Kamal Gupta
• Keywords: CCCG 2007, Computational Geometry, Polygon, Polygon Edge, Watchman Route Problem