Traversing Directed Eulerian Mazes

Abstract

The paper describes two algorithms for threading unknown, finite directed Eulerian mazes. Each of these algorithms is performed by a traveling robot whose control is a finite-state automaton. It is assumed that each vertex has a circular list of its outgoing edges. The items of this list are called exits. Each of the algorithms puts in one of the exits of each vertex a scan pebble. These pebbles can be used by a simple robot as traffic signals, which allow it to traverse an Eulerian cycle of the maze. For a directed graph (maze) G(V,E), the simple algorithm performs O(|V| ·|E|) edge traversals, while the advanced algorithm traverses every edge three times. Let d_out(v) be the out-degree of vertex v. The algorithms use, at each vertex v, a local memory of size O(logd_out(v)).