Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Piecemeal graph exploration by a mobile robot
Information and Computation
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
Journal of Graph Theory
Label-guided graph exploration by a finite automaton
ACM Transactions on Algorithms (TALG)
Note: Setting port numbers for fast graph exploration
Theoretical Computer Science
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
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
The reduced automata technique for graph exploration space lower bounds
Theoretical Computer Science
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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We consider the problem of periodic graph exploration in which a mobile entity with (at most) constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identified by different integer labels called port numbers. We are interested in the minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily, see [1]. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. [2] described an algorithm for assigning port numbers, and an oblivious agent (i.e., an agent with no persistent memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was proved in [3] to be no more than 3.75n (using a different assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most $4\frac{1}{3}n$ for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Finally, we give the first non-trivial lower bound, 2.8n, on the period length for the oblivious case.