Abstract

S. Koenig, A. Mudgal and C. Tovey. A Near-Tight Approximation Lower Bound and Algorithm for the Kidnapped Robot Problem. InAbstract: Localization is a fundamental problem in robotics. The 'kidnapped robot'
possesses a compass and map of its environment; it must determine its location
at a minimum cost of travel distance. The problem is NP-hard even to minimize
within factor c log n, where n is the number of vertices. No approximation
algorithm has been known. We give a O(log^{3} n)-factor algorithm. The
key idea is to plan travel in a 'majority-rule' map, which eliminates
uncertainty and permits a link to the 1/2-Group Steiner (not Group Steiner)
problem. The approximation factor is not far from optimal: we prove a c
log^{2-ε} n lower bound, assuming NP ⊄
ZTIME(n^{polylog(n)}), for the grid graphs commonly used in
practice. We also introduce a new hypothesis equivalence decomposition of the
plane, built from pairs of aspect graph duals, in order to extend the
algorithm to polygonal maps.

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This page was automatically created by a bibliography maintenance system that was developed as part of an undergraduate research project, advised by Sven Koenig.