## Abstract

A graph G= (V, E) is a geometric intersection graph if every node v∈ V is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph classes have been studied from both the theoretical and practical point of view. On the one hand, many hard problems can be efficiently solved or approximated when the input graph is restricted to a geometric intersection class of graphs. On the other hand, these graphs appear naturally in many applications such as sensor networks, scheduling problems, and others. Recently, in the context of distributed certification and distributed interactive proofs, the recognition of graph classes has started to be intensively studied. Different results related to the recognition of trees, bipartite graphs, bounded diameter graphs, triangle-free graphs, planar graphs, bounded genus graphs, H-minor free graphs, etc., have been obtained. The goal of the present work is to design efficient distributed protocols for the recognition of relevant geometric intersection graph classes, namely permutation graphs, trapezoid graphs, circle graphs and polygon-circle graphs. More precisely, for the two first classes we give proof labeling schemes recognizing them with logarithmic-sized certificates. For the other two classes, we give three-round distributed interactive protocols that use messages and certificates of size O(log n). Finally, we provide logarithmic lower-bounds on the size of the certificates on the proof labeling schemes for the recognition of any of the aforementioned geometric intersection graph classes.

Original language | English |
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Title of host publication | Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings |

Editors | Merav Parter |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 212-233 |

Number of pages | 22 |

ISBN (Print) | 9783031099922 |

DOIs | |

State | Published - 2022 |

Externally published | Yes |

Event | 29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 - Paderborn, Germany Duration: 27 Jun 2022 → 29 Jun 2022 |

### 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 | 13298 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 |
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Country/Territory | Germany |

City | Paderborn |

Period | 27/06/22 → 29/06/22 |

## Keywords

- Distributed decision
- Distributed interactive proofs
- Intersection Graph Classes
- Proof-labeling scheme