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We investigate the exploration and mapping of anonymous graphs by a mobileagent. It is long known that, without global information about the graph, it isnot possible to make the agent halt after the exploration except if the graphis a tree. We therefore endow the agent with binoculars, a sensing device thatcan show the local structure of the environment at a constant distance of theagent's current location and investigate networks that can be efficientlyexplored in this setting.  In the case of trees, the exploration without binoculars is fast (i.e. usinga DFS traversal of the graph, there is a number of moves linear in the numberof nodes). We consider here the family of Weetman graphs that is ageneralization of the standard family of chordal graphs and present a newdeterministic algorithm that realizes Exploration of any Weetman graph, withoutknowledge of size or diameter and for any port numbering. The number of movesis linear in the number of nodes, despite the fact that Weetman graphs are notsparse, some having a number of edges that is quadratic in the number of nodes.  At the end of the Exploration, the agent has also computed a map of theanonymous graph.

Using Binoculars for Fast Exploration and Map Construction in Chordal Graphs and Extensions