Stoffel, Edgar-Philipp (2009): Hierarchical Graphs as Organisational Principle and Spatial Model Applied to Pedestrian Indoor Navigation. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

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**DOI**: 10.5282/edoc.10620

### Abstract

In this thesis, hierarchical graphs are investigated from two different angles – as a general modelling principle for (geo)spatial networks and as a practical means to enhance navigation in buildings. The topics addressed are of interest from a multi-disciplinary point of view, ranging from Computer Science in general over Artiﬁcial Intelligence and Computational Geometry in particular to other ﬁelds such as Geographic Information Science. Some hierarchical graph models have been previously proposed by the research community, e.g. to cope with the massive size of road networks, or as a conceptual model for human wayﬁnding. However, there has not yet been a comprehensive, systematic approach for modelling spatial networks with hierarchical graphs. One particular problem is the gap between conceptual models and models which can be readily used in practice. Geospatial data is commonly modelled - if at all - only as a ﬂat graph. Therefore, from a practical point of view, it is important to address the automatic construction of a graph hierarchy based on the predominant data models. The work presented deals with this problem: an automated method for construction is introduced and explained. A particular contribution of my thesis is the proposition to use hierarchical graphs as the basis for an extensible, ﬂexible architecture for modelling various (geo)spatial networks. The proposed approach complements classical graph models very well in the sense that their expressiveness is extended: various graphs originating from different sources can be integrated into a comprehensive, multi-level model. This more sophisticated kind of architecture allows for extending navigation services beyond the borders of one single spatial network to a collection of heterogeneous networks, thus establishing a meta-navigation service. Another point of discussion is the impact of the hierarchy and distribution on graph algorithms. They have to be adapted to properly operate on multi-level hierarchies. By investigating indoor navigation problems in particular, the guiding principles are demonstrated for modelling networks at multiple levels of detail. Complex environments like large public buildings are ideally suited to demonstrate the versatile use of hierarchical graphs and thus to highlight the beneﬁts of the hierarchical approach. Starting from a collection of ﬂoor plans, I have developed a systematic method for constructing a multi-level graph hierarchy. The nature of indoor environments, especially their inherent diversity, poses an additional challenge: among others, one must deal with complex, irregular, and/or three-dimensional features. The proposed method is also motivated by practical considerations, such as not only ﬁnding shortest/fastest paths across rooms and ﬂoors, but also by providing descriptions for these paths which are easily understood by people. Beyond this, two novel aspects of using a hierarchy are discussed: one as an informed heuristic exploiting the speciﬁc characteristics of indoor environments in order to enhance classical, general-purpose graph search techniques. At the same time, as a convenient by- product of this method, clusters such as sections and wings can be detected. The other reason is to better deal with irregular, complex-shaped regions in a way that instructions can also be provided for these spaces. Previous approaches have not considered this problem. In summary, the main results of this work are: • hierarchical graphs are introduced as a general spatial data infrastructure. In particular, this architecture allows us to integrate different spatial networks originating from different sources. A small but useful set of operations is proposed for integrating these networks. In order to work in a hierarchical model, classical graph algorithms are generalised. This ﬁnding also has implications on the possible integration of separate navigation services and systems; • a novel set of core data structures and algorithms have been devised for modelling indoor environments. They cater to the unique characteristics of these environments and can be speciﬁcally used to provide enhanced navigation in buildings. Tested on models of several real buildings from our university, some preliminary but promising results were gained from a prototypical implementation and its application on the models.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | "graph,hierarchy,navigation,indoor,pedestrian,path finding,planning,multi-modal" |

Subjects: | 500 Natural sciences and mathematics > 510 Mathematics 500 Natural sciences and mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 2. June 2009 |

1. Referee: | Ohlbach, Hans Jürgen |

MD5 Checksum of the PDF-file: | 36006be1206b1e41f2230ab8c58cfd34 |

Signature of the printed copy: | 0001/UMC 18358 |

ID Code: | 10620 |

Deposited On: | 23. Feb 2010 07:44 |

Last Modified: | 24. Oct 2020 05:47 |