We introduce a dynamic prioritization scheme for parallel traversal of an irregularly structured spatio-temporal graph by multiple collaborative agents. We are concerned in particular with parallel execution of a sparse or fast algorithm for, but not limited to, an all-to-all transformation by multiple threads on a multi-core or manycore processor. Such fast algorithms play an escalating role a...

The temporal aggregation in temporal databases is an extension of the conventional aggregation including the time as a range condition of the aggregation. In this paper, we propose a new tree based structure for the temporal aggregation, called the CTA-tree. In the CTA-tree, we transform the time interval of a temporal data record into a value, called the T-value, using the Corner transformatio...

It’s a well-known fact that new GIS applications need to keep track of temporal information. However, the most widely used spatial index, the R-Tree and its variants, do not preserve the evolution of bounding boxes. Some new indexing structures were proposed in the literature that allows the retrieving of present and past states of data. In this paper we evaluate the most popular indexes struct...

We consider generalisations of tree width to directed graphs, that attracted much attention in the last fifteen years. About their relative strength with respect to “bounded width in one measure implies bounded width in the other” many problems remain unsolved. Only some results separating directed width measures are known. We give an almost complete picture of this relation. For this, we consi...

We introduce a temporal Steiner network problem in which a graph, as well as changes to its edges and/or vertices over a set of discrete times, are given as input; the goal is to find a minimal subgraph satisfying a set of k time-sensitive connectivity demands. We show that this problem, k-Temporal Steiner Network (k-TSN), is NP-hard to approximate to a factor of k − , for every fixed k ≥ 2 and...

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width is characterised by a game known as the cops-and-robber game where a number of cops chase a robber on the graph. We consider the natural adaptation of this game to directed graphs and show that monotone st...

Typically, geospatial data include satellite imagery, digital orthophoto quads, maps, digital line graphs, census data, voter registration, land ownership data, and land use data. This data is considered sensitive based on its location (characterized by its longitude and latitude), resolution, and the time of capture, among others. Since both objects and authorizations are associated with spati...

A directed graph can model any ordered relationship between objects. However, visualizing such graphs can be a challenging task. If the graph is undirected, a popular strategy is to choose a significant spanning tree, nominate a vertex as the root, for example the vertex whose distance from all other vertices is minimal, hang the significant spanning subtrees from this root and add in the remai...

Partial order temporal logics interpreted on trace systems have been shown not to have finitary complete axiomatizations due to the fact that the complexity of their decidability problem is in 11. This paper gives infinitary complete proof systems for several temporal logics on trace systems e.g. Computation Tree Logic with past operators and an essential subset of Interleaving Set Temporal Logic.

A complete axiomatic system CTL rp is introduced for a temporal logic for nitely branching ! +-trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL into CTL rp. In particular, that yields a complete axiomatization for the translations of all valid CTL-formulae. Thus, the temporal ...