We present the first constant‐factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an $O(1)$‐approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic‐factor approximations follow from set cover results, our new results exploit the geometric structure of terrains to obtain a substantially improved approximation algorithm.
25 June 2015 in NAVIGATION: Journal of the Institute of Navigation
SUMMARY: We introduce a novel probabilistic algorithm (CPRM) for real-time motion planning in the configuration space ${\EuScript C}$ . Our algorithm differs from a probabilistic road map (PRM) algorithm in the motion between a pair of anchoring points (local planner) which takes place on the boundary of the obstacle subspace ${\EuScript O}$ . We define a varying potential fieldfon ∂ ${\EuScript O}$ as a Morse function and follow $\vec{\nabla} f$ . We then exemplify our algorithm on a redundant worm climbing robot withndegrees of freedom and compare our algorithm running results with those of the PRM.