Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadra... more Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γtO,γ1] values that result in non-planar graphs. For β = 1, we show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n 2) time. Research supported in part by the CNR Project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed al CAD”, the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%), by Gen. Cat. SGR000356 and MEC-DGES-SEUID PB98-0933, Spain, and by NSERC, Canada.
... una rete virtuale di relazioni tra gli AS, la cui visualizzazione è di grande interesse per g... more ... una rete virtuale di relazioni tra gli AS, la cui visualizzazione è di grande interesse per gli Internet Service Provider (ISP) 1 . Dall ... Elettronica e dell'Informazione) dell'Università di Perugia, coordinato dagli autori di questo report, opera da anni nel settore della visualizzazione dell ...
ABSTRACT The reliability of a network is often described by its robustness under errors or attack... more ABSTRACT The reliability of a network is often described by its robustness under errors or attacks. The robustness of many complex networks has been understood from their scale-free structure. Indeed, scale-free networks are typically resilient to random failures, while vulnerable to targeted attacks. Neverthe-less, the progress of building a robust network in the development of a biological neural network has not been studied because of the lack of proper data. Here, we examined the robustness of a simplified neural circuitry built from about ten thousand single neurons of the Drosophila brain; we found the network is resilient under both errors and attacks. Furthermore, we observe how such a resiliency is associated with the accumulation of neurons along their birth stages. Being able to understand and replicate the conditions behind such a robust structure would have a great impact in designing reliable networks in different application domains.
The paper describes WhatsOnWeb+, a search clustering engine that allows users to browse and analy... more The paper describes WhatsOnWeb+, a search clustering engine that allows users to browse and analyze the results of a query by means of enhanced graph visualization techniques. WhatsOnWeb+ integrates a wide array of visual interfaces, animation and interaction functionalities, and clustering technologies. The effectiveness of the different visual interfaces and of the different clustering algorithms implemented in the system has
The recent interest in three-dimensional graph drawing has been motivating studies on how to exte... more The recent interest in three-dimensional graph drawing has been motivating studies on how to extend two-dimensional techniques to higher dimensions. A common 2D approach for computing an orthogonal drawing separates the task of defining the shape of the drawing from the task of computing its coordinates. First results towards finding a three-dimensional counterpart of this approach are presented by G. Di Battista,
In this paper we deal with the problem of computing upward two-page book embeddings of Two Termin... more In this paper we deal with the problem of computing upward two-page book embeddings of Two Terminal Series-Parallel (TTSP) digraphs, which are a subclass of series-parallel digraphs. An optimal O(n) time and space algorithm to compute an upward two-page book embedding of a TTSP-digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n3)
ABSTRACT A 2-layer drawing represents a bipartite graph where each vertex is a point on one of tw... more ABSTRACT A 2-layer drawing represents a bipartite graph where each vertex is a point on one of two parallel lines, no two vertices on the same line are adjacent, and the edges are straight-line segments. In this paper we study 2-layer drawings where any two crossing edges meet at right angle. We characterize the graphs that admit this type of drawing, provide linear-time testing and embedding algorithms, and present a polynomial-time crossing minimization technique. Also, for a given graph G and a constant k, we prove that it is $\mathcal{NP}$ -complete to decide whether G contains a subgraph of at least k edges having a 2-layer drawing with right angle crossings.
Information Visualization is a widespread approach of the Information and Communication Technolog... more Information Visualization is a widespread approach of the Information and Communication Technologies, and it facilitates the manipulation of abstract information by representing it by geometric models. It has been shown that spatial representation can be independent by the ...
Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadra... more Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γtO,γ1] values that result in non-planar graphs. For β = 1, we show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n 2) time. Research supported in part by the CNR Project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed al CAD”, the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%), by Gen. Cat. SGR000356 and MEC-DGES-SEUID PB98-0933, Spain, and by NSERC, Canada.
... una rete virtuale di relazioni tra gli AS, la cui visualizzazione è di grande interesse per g... more ... una rete virtuale di relazioni tra gli AS, la cui visualizzazione è di grande interesse per gli Internet Service Provider (ISP) 1 . Dall ... Elettronica e dell'Informazione) dell'Università di Perugia, coordinato dagli autori di questo report, opera da anni nel settore della visualizzazione dell ...
ABSTRACT The reliability of a network is often described by its robustness under errors or attack... more ABSTRACT The reliability of a network is often described by its robustness under errors or attacks. The robustness of many complex networks has been understood from their scale-free structure. Indeed, scale-free networks are typically resilient to random failures, while vulnerable to targeted attacks. Neverthe-less, the progress of building a robust network in the development of a biological neural network has not been studied because of the lack of proper data. Here, we examined the robustness of a simplified neural circuitry built from about ten thousand single neurons of the Drosophila brain; we found the network is resilient under both errors and attacks. Furthermore, we observe how such a resiliency is associated with the accumulation of neurons along their birth stages. Being able to understand and replicate the conditions behind such a robust structure would have a great impact in designing reliable networks in different application domains.
The paper describes WhatsOnWeb+, a search clustering engine that allows users to browse and analy... more The paper describes WhatsOnWeb+, a search clustering engine that allows users to browse and analyze the results of a query by means of enhanced graph visualization techniques. WhatsOnWeb+ integrates a wide array of visual interfaces, animation and interaction functionalities, and clustering technologies. The effectiveness of the different visual interfaces and of the different clustering algorithms implemented in the system has
The recent interest in three-dimensional graph drawing has been motivating studies on how to exte... more The recent interest in three-dimensional graph drawing has been motivating studies on how to extend two-dimensional techniques to higher dimensions. A common 2D approach for computing an orthogonal drawing separates the task of defining the shape of the drawing from the task of computing its coordinates. First results towards finding a three-dimensional counterpart of this approach are presented by G. Di Battista,
In this paper we deal with the problem of computing upward two-page book embeddings of Two Termin... more In this paper we deal with the problem of computing upward two-page book embeddings of Two Terminal Series-Parallel (TTSP) digraphs, which are a subclass of series-parallel digraphs. An optimal O(n) time and space algorithm to compute an upward two-page book embedding of a TTSP-digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n3)
ABSTRACT A 2-layer drawing represents a bipartite graph where each vertex is a point on one of tw... more ABSTRACT A 2-layer drawing represents a bipartite graph where each vertex is a point on one of two parallel lines, no two vertices on the same line are adjacent, and the edges are straight-line segments. In this paper we study 2-layer drawings where any two crossing edges meet at right angle. We characterize the graphs that admit this type of drawing, provide linear-time testing and embedding algorithms, and present a polynomial-time crossing minimization technique. Also, for a given graph G and a constant k, we prove that it is $\mathcal{NP}$ -complete to decide whether G contains a subgraph of at least k edges having a 2-layer drawing with right angle crossings.
Information Visualization is a widespread approach of the Information and Communication Technolog... more Information Visualization is a widespread approach of the Information and Communication Technologies, and it facilitates the manipulation of abstract information by representing it by geometric models. It has been shown that spatial representation can be independent by the ...
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Papers by G. Liotta