Amortized efficiency of list update and paging rules
Communications of the ACM
Representing and acquiring geographic knowledge
Representing and acquiring geographic knowledge
Location estimation and uncertainty analysis for mobile robots
Autonomous robot vehicles
Theoretical Computer Science
The robot localization problem in two dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
A layered architecture for office delivery robots
AGENTS '97 Proceedings of the first international conference on Autonomous agents
Localizing a Robot with Minimum Travel
SIAM Journal on Computing
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
The Cricket location-support system
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Gridworlds as Testbeds for Planning with Incomplete Information
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Randomized Algorithms for Minimum Distance Localization
International Journal of Robotics Research
Cost-effective active localization technique for mobile robots
ROBIO'09 Proceedings of the 2009 international conference on Robotics and biomimetics
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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 [6] even to minimize within factor c log n[21], where n is the number of vertices. No approximation algorithm has been known. We give a O(log3 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 log2-ε n lower bound, assuming NP ⊈ ZTIME(npolylog(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.