Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Polylogarithmic-overhead piecemeal graph exploration
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
The full degree spanning tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Piecemeal graph exploration by a mobile robot
Information and Computation
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
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Tree exploration with little memory
Journal of Algorithms
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
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
Setting port numbers for fast graph exploration
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
On the Power of Local Orientations
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Anonymous graph exploration without collision by mobile robots
Information Processing Letters
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We consider the problem of periodic exploration of all nodes in undirected graphs by using a finite state automaton called later a robot. The robot, using a constant number of states (memory bits), must be able to explore any unknown anonymous graph. The nodes in the graph are neither labelled nor colored. However, while visiting a node v the robot can distinguish between edges incident to it. The edges are ordered and labelled by consecutive integers 1, . . . , d(v) called port numbers, where d(v) is the degree of v. Periodic graph exploration requires that the automaton has to visit every node infinitely many times in a periodic manner. Note that the problem is unsolvable if the local port numbers are set arbitrarily, see [8]. In this context, we are looking for the minimum function π(n), such that, there exists an efficient deterministic algorithm for setting the local port numbers allowing the robot to explore all graphs of size n along a traversal route with the period π(n). Dobrev et al. proved in [13] that for oblivious robots π(n) ≤ 10n. Recently Ilcinkas proposed another port labelling algorithm for robots equipped with two extra memory bits, see [20], where the exploration period π(n) ≤ 4n-2. In the same paper, it is conjectured that the bound 4n - O(1) is tight even if the use of larger memory is allowed. In this paper, we disprove this conjecture presenting an efficient deterministic algorithm arranging the port numbers, such that, the robot equipped with a constant number of bits is able to complete the traversal period in π(n) ≤ 3.75n -2 steps hence decreasing the existing upper bound. This reduces the gap with the lower bound of π(n) ≥ 2n - 2 holding for any robot.