On the valid deterministic localization plan problem

Abstract

Grid graphs are popular testbeds for planning with incomplete information. In particular, it is studied a fundamental planning problem, localization, to investigate whether gridworlds make good testbeds for planning with incomplete information. It is found empirically that greedy planning methods that interleave planning and plan execution can localize robots very quickly on random gridworlds or mazes. Thus, they may not provide adequately challenging testbeds. On the other hand, it is showed that finding localization plans that are within a log factor of optimal is NP-hard. Thus there are instances of gridworlds on which all greedy planning methods perform very poorly. These theoretical results help empirical researchers to select appropriate planning methods for planning with incomplete information as well as testbeds to demonstrate them. However, for practical application of difficult instances we need a method for their fast decision. In this paper, we consider an approach to solve localization problem. In particular, we consider an explicit polynomial reduction from the decision version of the valid deterministic localization plan problem to the 3-satisfiability problem. Mathematics Subject Classification: 68T40