Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition

Let $\mathcal{D}$ be a set of $n$ pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set $P$ containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of $P$. Our data structure can be built in $O(n \log n)$ time and has linear size. Given $P$, we can find its onion decomposition in $O(n \log k)$ time, where $k$ is the number of layers. We also provide a matching lower bound. Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onionComment: 10 pages, 5 figures; a preliminary version appeared at WADS 201

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce