Fast Periodic Graph Exploration with Constant Memory

We consider the problem of periodic exploration of all nodes in undirected graphs by using a nite 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 innitely 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 ecient 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 ...

• Type: Conference
• Year: 2007
• Where: SIROCCO
• Authors: Leszek Gasieniec, Ralf Klasing, Russell A. Martin, Alfredo Navarra, Xiaohui Zhang
• Keywords: Ecient Deterministic Algorithm, Information Technology, Local Port Numbers, Port Numbers, SIROCCO 2007