Anonymous Graph Exploration with Binoculars

TL;DR

This paper introduces binoculars as a sensing device for mobile agents, enabling exploration and halting in many non-tree networks by providing local structural information, with a complete characterization and a universal exploration algorithm.

Contribution

It presents the first comprehensive characterization of networks explorable with binoculars and provides a universal exploration algorithm for these networks.

Findings

Binoculars enable exploration of a large class of non-tree networks.

A complete characterization of explorable networks with binoculars is provided.

A universal exploration algorithm is developed that halts in explorable networks and does not halt otherwise.

Abstract

We investigate the exploration of networks by a mobile agent. It is long known that, without global information about the graph, it is not possible to make the agent halts after the exploration except if the graph is a tree. We therefore endow the agent with binoculars, a sensing device that can show the local structure of the environment at a constant distance of the agent current location. We show that, with binoculars, it is possible to explore and halt in a large class of non-tree networks. We give a complete characterization of the class of networks that can be explored using binoculars using standard notions of discrete topology. Our characterization is constructive, we present an Exploration algorithm that is universal; this algorithm explores any network explorable with binoculars, and never halts in non-explorable networks.