### Abstract

Efficient exploration of unknown or unmapped environments has become one of the fundamental problem domains in algorithm design. Its applications range from robot navigation in hazardous environments to rigorous searching, indexing and analysing digital data available on the Internet. A large number of exploration algorithms has been proposed under various assumptions about the capability of mobile (exploring) entities and various characteristics of the environment which are to be explored. This paper considers the graph model, where the environment is represented by a graph of connections in which discrete moves are permitted only along its edges. Designing efficient exploration algorithms in this model has been extensively studied under a diverse set of assumptions, e.g., directed vs undirected graphs, anonymous nodes vs nodes with distinct identities, deterministic vs probabilistic solutions, single vs multiple agent exploration, as well as in the context of different complexity measures including the time complexity, the memory consumption, and the use of other computational resources such as tokens and messages. In this work the emphasis is on memory efficient exploration of anonymous graphs. We discuss in more detail three approaches: random walk, Propp machine and basic walk, reviewing major relevant results, presenting recent developments, and commenting on directions for further research.

Original language | English (US) |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers |

Pages | 14-29 |

Number of pages | 16 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

Event | 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 - Durham, United Kingdom Duration: Jun 30 2008 → Jul 2 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5344 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 |
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Country | United Kingdom |

City | Durham |

Period | 6/30/08 → 7/2/08 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers*(pp. 14-29). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5344 LNCS). https://doi.org/10.1007/978-3-540-92248-3_2