Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Approximation algorithms for lawn mowing and milling
Computational Geometry: Theory and Applications
Competitive on-line coverage of grid environments by a mobile robot
Computational Geometry: Theory and Applications
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Not being (super)thin or solid is hard: A study of grid Hamiltonicity
Computational Geometry: Theory and Applications
Exploring simple grid polygons
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Optimal exploration of terrains with obstacles
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Worst-case optimal exploration of terrains with obstacles
Information and Computation
Fast collaborative graph exploration
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We study the problem of exploring a simple grid polygon using a mobile robot. The robot starts from a location which is adjacent to the boundary of the polygon, and after exploring all the squares, has to return to its starting location. The robot is equipped with memory, but has no prior knowledge of the explored terrain. The view of the terrain is restricted to the four squares directly adjacent to the robot's current location. The performance of the exploration strategy is measured in terms of the competitive ratio, with respect to the length of the optimal path for an exploration with complete knowledge of the terrain. We propose a new exploration strategy which achieves a competitive ratio of 5/4, whereas the previously best approach [Icking, Kamphans, Klein, and Langetepe; Proc. COCOON'05] has a competitive ratio of 4/3. The analysis for our algorithm is tight. Moreover, we show that no exploration strategy is ever better than 20/17-competitive, thus improving the previous lower bound of 7/6.