Pier Francesco Cortese

C-Planarity of C-Connected Clustered Graphs

We present the first characterization of c-planarity for c-connected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we provide a linear-time c-planarity testing and embedding algorithm for c-connected clustered graphs. The algorithm is reasonably easy to implement, since it exploits as building blocks simple algorithmic tools like the computation of lowest common ancestors, minimum and maximum spanning trees, and counting sorts. It also makes use of well-known data structures as SPQR-trees and BC-trees. If the test fails, the algorithm identifies a structural element responsible for the non-cplanarity of the input clustered graph.

Topographic Visualization of Prefix Propagation in the Internet

We propose a new metaphor for the visualization of prefixes propagation in the Internet. Such a metaphor is based on the concept of topographic map and allows to put in evidence the relative importance of the Internet Service Providers (ISPs) involved in the routing of the prefix. Based on the new metaphor we propose an algorithm for computing layouts and experiment with such algorithm on a test suite taken from the real Internet. The paper extends the visualization approach of the BGPlay service, which is an Internet routing monitoring tool widely used by ISP operators

Efficient and practical authentication of PUF-based RFID tags in supply chains

We propose new methodologies for the authentication of RFID tags along supply chains, exploiting tags equipped with a Physical Unclonable Function (PUF) device. Unlike state-of-the-art approaches that require sharing a large database of challenge-response pairs (CRPs), we achieve a constant amount of shared secret data, oblivious of the number of CRPs and tags to be handled. Such data can be distributed using a secure hardware token. The rest of the data can be released over an insecure one-way communication channel that can be realized by shipping storage media along with goods. We discuss the applicative scenario and perform experiments on pre-production PUF-based tags in order to assess the applicability of our approaches.

Clustered planarity

A cluster of a graph is a non empty subset of vertices. A clustered graph C(G, T ) is a graph G plus a rooted tree T such that the leaves of T are the vertices of G (see Fig. 1 for an example). Each internal node ν of T corresponds to the cluster V (ν) of G whose vertices are the leaves of the subtree rooted at ν. The subgraph of G induced by V (ν) is denoted as G(ν). An edge e between a vertex of V (ν) and a vertex of V − V (ν) is said to be incident on ν. Graph G and tree T are called underlying graph and inclusion tree, respectively. Drawing a clustered graph is requided in many applications. To give a few examples:

Stop Minding Your P's and Q's: Implementing a Fast and Simple DFS-based Planarity Testing and Embedding Algorithm

In this paper we give a new description of the planarity testing and embedding algorithm presented by Boyer and Myrvold [2], providing, in our opinion, new insights on the combinatorial foundations of the algorithm. Especially, we give a detailed illustration of a fundamental phase of the algorithm, called walk-up, which was only succinctly illustrated in [2]. Also, we present an implementation of the algorithm and extensively test its efficiency against the most popular implementations of planarity testing algorithms. Further, as a side effect of the test activity, we propose a general overview of the state of the art (restricted to efficiency issues) of the planarity testing and embedding field.

Clustering cycles into cycles of clusters

In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are “highly non connected”. We start by studying 3-cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the c-planarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3-cluster cycles in terms of formal grammars. Finally, we generalize the results on 3-cluster cycles considering clustered graphs that at each level of the inclusion tree have a cycle structure. Even in this case we show efficient c-planarity testing and drawing algorithms.

On embedding a cycle in a plane graph

Consider a planar drawing

Topological Morphing of Planar Graphs

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On the topologies of local minimum spanning trees

of a planar graph G such that the vertices are drawn as small circles and the edges are drawn as thin strips. Consider a cycle c of G. Is it possible to draw c as a non-intersecting closed curve inside

Clustering Cycles into Cycles of Clusters

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