Proof and More Variations of Bellman's Lost-in-a-forest Problem

Abstract

In this paper, based on our previous general formulation and computational solution to Bellman's Lost-in-a-forest Problem, we provide the proof of general solution and obtained more variations and results related to this problem. This paper provides generalized formalized method connecting curve covering, lost-in-the-forest problem, and traveling salesman problem with neighborhoods. We prove the equivalence and convergence. We also provide more results of searching for two lines, connection to Wetzel's unit arc covering problem, variations with closed path, variations in three dimensions, etc. The results include general calculation equations, partial analytical results, and numerical results.