How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
Polylogarithmic-overhead piecemeal graph exploration
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Optimal robot localization in trees
Information and Computation
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Performance bounds for planning in unknown terrain
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Tree exploration with little memory
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
Information and Computation
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
An optimal competitive strategy for walking in streets
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Mobile agent rendezvous: a survey
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Online routing in faulty meshes with sub-linear comparative time and traffic ratio
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Tree exploration with an oracle
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Optimal exploration of terrains with obstacles
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Online multi-path routing in a maze
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Survey: Online algorithms for searching and exploration in the plane
Computer Science Review
Collecting information by power-aware mobile agents
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Worst-case optimal exploration of terrains with obstacles
Information and Computation
Planning for provably reliable navigation using an unreliable, nearly sensorless robot
International Journal of Robotics Research
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Consider a robot that has to travel from a start location $s$ to a target $t$ in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from $s$ to $t$ to the length of the shortest (obstacle-free) path between $s$ and $t$ in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with nonconvex obstacles, which are related to the study of maze traversal. We also show scenes where randomized algorithms are provably better than deterministic algorithms.