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
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
Fast periodic graph exploration with constant memory
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
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
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Synchronization Helps Robots to Detect Black Holes in Directed Graphs
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Synchronous black hole search in directed graphs
Theoretical Computer Science
More efficient periodic traversal in anonymous undirected graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
More efficient periodic traversal in anonymous undirected graphs
Theoretical Computer Science
Finding patterns in an unknown graph
AI Communications - The Symposium on Combinatorial Search
Hi-index | 0.00 |
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 coloured. 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. In this paper, we are interested in minimisation of the length of the exploration period. In other words, we want to minimise the maximum number of edge traversals performed by the robot between two consecutive visits of a generic node, in the same state and entering the node by the same port. Note that the problem is unsolvable if the local port numbers are set arbitrarily, see [L. Budach, Automata and labyrinths, Math. Nachr. 86 (1978) 195-282]. In this context, we are looking for the minimum function @p(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 @p(n). Dobrev et al. proved in [S. Dobrev, J. Jansson, K. Sadakane, W.-K. Sung, Finding short right-hand-on-the-wall walks in graphs, in: Proc. 12th Colloquium on Structural Information and Communication Complexity, SIROCCO 2005, in: Lecture Notes in Comput. Sci., vol. 3499, Springer, Berlin, 2005, pp. 127-139] that for oblivious robots @p(n)==2n-2 holding for any robot.