Related papers: Windows into Geometric Events: Data Structures for…
We consider the problem of analyzing social network data sets in which the edges of the network have timestamps, and we wish to analyze the subgraphs formed from edges in contiguous subintervals of these timestamps. We provide data…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
We present new results on a number of fundamental problems about dynamic geometric data structures: 1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or…
Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…
Spatial data structures allow to make efficient queries on Geographical Information Systems (GIS). Spatial queries involve the geometry of the data, such as points, lines, or polygons. For instance, a spatial query could poll for the…
Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where $\tau$ could be a time point or time interval. Temporal knowledge graphs may exhibit…
In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
Constructing complex queries on data which combines spatial, temporal, and spectral aspects is a challenging and error-prone process. Query interfaces of general-purpose database management systems fall short in providing intuitive support…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
The crease set of an event horizon is studied in a spacetime with discrete or continuous symmetry. It determines possible topologies on spatial sections of an event horizon. We thereby investigate the classification of stable topological…
We present the first fully dynamic connectivity data structures for geometric intersection graphs achieving constant query time and sublinear amortized update time for most types of geometric objects in 2D. Our data structures can answer…
In this paper, we focus on temporal property graphs, that is, property graphs whose labeled nodes and edges as well as the values of the properties associated with them may change with time. For instance, consider a bibliographic network,…
We consider the problem of dynamically maintaining the convex hull of a set $S$ of points in the plane under the following special sequence of insertions and deletions (called {\em window-sliding updates}): insert a point to the right of…
We consider various data-analysis queries on two-dimensional points. We give new space/time tradeoffs over previous work on geometric queries such as dominance and rectangle visibility, and on semigroup and group queries such as sum,…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…
We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge…
We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…
In this paper we study skyline queries in the distributed computational model, where we have $s$ remote sites and a central coordinator (the query node); each site holds a piece of data, and the coordinator wants to compute the skyline of…
Shape is a powerful tool to understand point sets. A formal notion of shape is given by $\alpha$-shapes, which generalize the convex hull and provide adjustable level of detail. Many real-world point sets have an inherent temporal property…