SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Optimal constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Multi-robot tree and graph exploration
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Computing without communicating: ring exploration by asynchronous oblivious robots
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Optimal map construction of an unknown torus
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Distributed security algorithms by mobile agents
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Power-Aware collective tree exploration
ARCS'06 Proceedings of the 19th international conference on Architecture of Computing Systems
Smart robot teams exploring sparse trees
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Distributed exploration of an unknown graph
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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A robot has to visit all nodes and traverse all edges of an unknown undirected connected graph, using as few edge traversals as possible. The quality of an exploration algorithm A is measured by comparing its cost (number of edge traversals) to that of the optimal algorithm having full knowledge of the graph. The ratio between these costs, maximized over all starting nodes in the graph and over all graphs in a given class U, is called the overhead of algorithm A for the class U of graphs. We construct natural exploration algorithms, for various classes of graphs, that have smallest, or - in one case - close to smallest, overhead. An important contribution of this paper is establishing lower bounds that prove optimality of these exploration algorithms.