We consider spatio-temporal databases supporting spatial objects with continuously changing position and extent, termed moving objects databases . We formally define a data model for such databases that includes complex evolving spatial structures such as line networks or multi-component regions with holes. The data model is given as a collection of data types and operations which can be plugged as attribute types into any DBMS data model (e.g. relational, or object-oriented) to obtain a complete model and query language. A particular novel concept is the sliced representation which represents a temporal development as a set of units , where unit types for spatial and other data types represent certain “simple” functions of time. We also show how the model can be mapped into concrete physical data structures in a DBMS environment.

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Abstract. Given an instance of an optimization problem together with an optimal solution, we consider the scenario in which this instance is modified locally. In graph problems, e. g., a singular edge might be removed or added, or an edge weight might be varied, etc. For a problem U and such a local modification operation, let lm-U (local-modification-U ) denote the resulting problem. The question is whether it is possible to exploit the additional knowledge of an optimal solution to the original instance or not, i. e., whether lm-U is computationally more tractable than U . Here, we give non-trivial examples both of problems where this is and problems where this is not the case. Our main results are these:1. The local modification to change the cost of a singular edge turns the traveling salesperson problem (TSP) into a problem lm-TSP which is as hard as TSP itself, i. e., unless P = N P , there is no polynomial-time p(n)-approximation algorithm for lm-TSP for any polynomial p. Moreover, lm-TSP where inputs must satisfy the β-triangle inequality (lm-∆ β -TSP) remains NP-hard for all β > 1 2 . 2. For lm-∆-TSP (i. e., metric lm-TSP), an efficient 1.4-approximation algorithm is presented. In other words, the additional information enables us to do better than if we simply used Christofides' algorithm for the modified input. 3. Similarly, for all 1 < β < 3.34899, we achieve a better approximation ratio for lm-∆ β -TSP than for ∆ β -TSP. 4. Metric TSP with deadlines (time windows), if a single deadline or the cost of a single edge is modified, exhibits the same lower bounds on the approximability in these local-modification versions as those currently known for the original problem.

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Given an n-vertex non-negatively real-weighted graph G, whose vertices are partitioned into a set of k clusters, a clustered network design problem on G consists of solving a given network design optimization problem on G, subject to some additional constraint on its clusters. In particular, we focus on the classic problem of designing a single-source shortest-path tree, and we analyze its computational hardness when in a feasible solution each cluster is required to form a subtree. We first study the unweighted case, and prove that the problem is NP-hard. However, on the positive side, we show the existence of an approximation algorithm whose quality essentially depends on few parameters, but which remarkably is an O(1)-approximation when the largest out of all the diameters of the clusters is either O(1) or Θ(n). Furthermore, we also show that the problem is fixed-parameter tractable with respect to k or to the number of vertices that belong to clusters of size at least 2. Then, we focus on the weighted case, and show that the problem can be approximated within a tight factor of O(n), and that it is fixed-parameter tractable as well. Finally, we analyze the unweighted single-pair shortest pathThe results presented in this work have been announced in a preliminary form in [6].

In order to bring informatics, its ideas and ways of thinking of major educational value to all primary and secondary school students, the Italian Inter-universities Consortium for Informatics (CINI), in collaboration with the academic associations who gather together researchers in informatics (GRIN) and computer engineering (GII), has recently proposed a core informatics curriculum for all the levels of compulsory school. This paper summarizes the proposed curriculum, highlights the key underlying motivations, and outlines a possible strategy to ensure that its implementation in schools can be effective.

Abstract. Formal methods based on the mathematical theory of partially ordered sets (i.e., posets) have been used in the database field for the modelling of spatial data since many years. In particular, the use of the lattice completion (or normal completion) of a poset has been shown by Kainz, Egenhofer and Greasley [13] to be a fundamental technique to build meaningful representations of spatial subdivisions. In fact, they proved that the new elements introduced by the normal completion process can (and have to) be interpreted as being the intersection of poset elements. This is fundamental, from a mathematical point of view, since it means that the lattice resulting from the normal completion is the closure of the given poset with respect to the intersection operation. In this paper we precisely clarify the limitations for the use of lattices as models for spatial subdivisions, by proving sufficient and necessary conditions. Our result gives therefore a sound theoretical basis for the use of lattices built on simplicial complexes as a data model for spatial databases.

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