Enrico Nardelli

A data model and data structures for moving objects databases

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.

A layout algorithm for data flow diagrams

A layout algorithm is presented that allows the automatic drawing of data flow diagrams, a diagrammatic representation widely used in the functional analysis of information systems. A grid standard is defined for such diagrams, and aesthetics for good readability are identified. The layout algorithm receives as input an abstract graph specifying connectivity relations between the elements of the diagram, and produces as output a corresponding diagram according to the aesthetics. The basic strategy is to build incrementally the layout; first, a good topology is constructed with few crossings between edges; subsequently, the shape of the diagram is determined in terms of angles appearing along edges. and finally dimensions are given to the graph, obtaining a grid skeleton for the diagram.

Algorithms for Moving Objects Databases

Whereas earlier work on spatiotemporal databases generally focused on geometries changing in discrete steps, the emerging area of moving objects databases supports geometries changing continuously. Two important abstractions are moving point and moving region, modelling objects for which only the time-dependent position, or also the shape and extent are relevant, respectively. Examples of the first kind of moving entity are all kinds of vehicles, aircraft, people or animals; of the latter hurricanes, forest fires, forest growth or oil spills in the sea. The goal is to develop data models and query languages as well as DBMS implementations supporting such entities, enabling new kinds of database applications. In earlier work we have proposed an approach based on

A faster computation of the most vital edge of a shortest path

Abstract Let P G (r,s) denote a shortest path between two nodes r and s in an undirected graph G=(V,E) such that |V|=n and |E|=m and with a positive real length w(e) associated with any e∈E . In this paper we focus on the problem of finding an edge e ∗ ∈P G (r,s) whose removal is such that the length of P G−e ∗ (r,s) is maximum, where G−e ∗ =(V,E⧹{e ∗ }) . Such an edge is known as the most vital edge of the path P G (r,s) . We will show that this problem can be solved in O (m·α(m,n)) time, where α is the functional inverse of the Ackermann function, thus improving on the previous O (m+n log n) time bound.

Hierarchies and planarity theory

In diagrammatic representations of hierarchies the minimization of the number of crossings between edges is a well-known criterion for improving readability. An efficient algorithm for testing if a hierarchy is planar (i.e. if it can be drawn without edge crossings) is proposed. A complete combinatorial characterization of the class of planar hierarchies is also given. >

Chorochronos: a research network for spatiotemporal database systems

* Andrew Frank, Stephane Grumbach, Ralf Hartmut Güting, Christian S. Jensen, Manolis Koubarakis, Nikos Lorentzos, Yannis Manolopoulos, Enrico Nardelli, Barbara Pernici, Hans-Jörg Schek, Michel Scholl, Timos Sellis, Babis Theodoulidis and Peter Widmayer. Contact author: Timos Sellis, Dept. of Electrical and Comp. Engin., National Tech. University of Athens, Zografou 15773, Athens, Greece, timos@dbnet.ece.ntua.gr

Abstract data types for the logical modeling of complex data

Abstract In this paper we propose a logical data model for complex data. Our proposal extends the relational model by using abstract data types for domains specification and an extended relational algebra is also introduced. The introduction of the parameterized type Geometry(S), where S is a ground set of elements, allows the representation of complex aggregated data. As an example, we discuss how our model supports the definition of geographical DBMSs. Moreover, to show the generality of our approach, we sketch how the model can be used in the framework of statistical applications.

Finding the detour-critical edge of a shortest path between two nodes

Abstract Let PG(r, s) denote a shortest path between two nodes r and s in an undirected graph G with nonnegative edge weights. A detour at a node u ϵ PG(r, s) = 〈r,…, u, v,…,s〉 is defined as a shortest path PG − e(u, s) from u to s which does not make use of (u, v). In this paper we focus on the problem of finding an edge e = (u, v) ϵ PG(r, s) whose removal produces a detour at node u such that the length of PG − e(u, s) minus the length of PG(u, s) is maximum. We call such an edge a detour-critical edge. We will show that this problem can be solved in O(m + n log n) time, where n and m denote the number of nodes and edges in the graph, respectively.

Finding the Most Vital Node of a Shortest Path

In an undirected, 2-node connected graph G= (V,E) with positive real edge lengths, the distance between anyt wo nodes r and s is the length of a shortest path between r and s in G. The removal of a node and its incident edges from G may increase the distance from r to s. A most vital node of a given shortest path from rto s is a node (other than r and s) whose removal from G results in the largest increase of the distance from r to s. In the past, the problem of finding a most vital node of a given shortest path has been studied because of its implications in network management, where it is important to know in advance which component failure will affect network efficiencythe most. In this paper, we show that this problem can be solved in O(m+ nlog n) time and O(m) space, where mand n denote the number of edges and the number of nodes in G.

Time and space efficient secondary memory representation of quadtrees

Abstract Efficient management of spatial data is becoming more and more important and for very large sets of 2-dimensional data, secondary memory data representations are required. An important class of queries for spatial data are those that extract a subset of the data: they are called window queries (also region or range queries). In this paper we propose and analyze a new data structure, namely the hybrid linear quadtree, for the efficient secondary memory processing of three kinds of window queries, that is the exist, the report and the select query. In particular we prove that for a window of size n × n in a feature space (e.g., an image) of size T × T using the hybrid linear quadtree stored on a B+-tree with bucket size r, the exist and report query can be answered with O(n logr T) accesses to secondary storage, while the select query can be answered with O(n log r T + n 2 r ) accesses to secondary storage. This is an improvement in worst-case I/O time complexity over previous results and shows that multiple non-overlapping features (i.e., coloured images) can be treated with the same I/O complexity as single features (i.e., black and white images). Furthermore, we show that the hybrid linear quadtree has a low space occupancy overhead with respect to the classic linear quadtree.