Exploring unknown environments
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Piecemeal graph exploration by a mobile robot
Information and Computation
Proceedings of the 4th GI-Conference on Theoretical Computer Science
Optimal graph exploration without good maps
Theoretical Computer Science
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Journal of Graph Theory
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
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
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We consider a network represented by a simple connected undirected graph with Nanonymous nodes that have local orientations, i.e. incident edges of each vertex have locally-unique labels --- port names.We define a pre-processing phase that enables a right-hand rule using agent (RH-agent) to traverse the entire graph. For this phase we design an algorithm for an agent that performs the precomputation. The agent will alter the network by modifying the local orientations using a simple operation of exchanging two local labels in each step. We show a polynomial-time algorithm for this precomputation that needs only one pebble and O(logN) memory in the agent.Furthermore we design a similar algorithm where the memory that the agent uses for the precomputation is decreased to O(1). In this case, the agent is not able to perform some operations by itself due to the lack of memory and needs support from the environment.