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 such that every point on the polygon boundary is visible from at least one viewpoint. 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. 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. The algorithm we propose first constructs a graph that connects O(n12) number of sample viewpoints 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-relaxation based algorithm we introduced in [27, 29]. We show that our algorithm has an approximation ratio in the order of either the view frequency, defined as the maximum number of sample viewpoints that cover a polygon edge, or a polynomial of log n, whichever is smaller. [ABSTRACT FROM AUTHOR]