Raphael Carlos Santos Machado

Total chromatic number of {square,unichord}-free graphs

Abstract We determine a surprising class for which edge-colouring is NP-complete but whose graphs are all Type 1. The class of unichord-free graphs was recently studied by Trotignon and Vuskovic [N. Trotignon and K. Vuskovic. A structure theorem for graphs with no cycle with a unique chord and its consequences . To appear in J. Graph Theory. (Available online at http://www.comp.leeds.ac.uk/vuskovi/chord.ps .)] in the context of vertex-colouring. Machado, Figueiredo and Vuskovic [R. C. S. Machado, C. M. H. de Figueiredo, and K. Vuskovic. Chromatic index of graphs with no cycle with unique chord . In: Proc. of the ALIO/EUROWorkshop on Applied Optimization (2008). Full paper submitted to Theoret. Comput. Sci.] established the NP-completeness of edge-colouring unichord-free graphs. For the subclass of {square,unichord}-free graphs, an interesting complexity dicothomy holds [R. C. S. Machado, C. M. H. de Figueiredo, and K. Vuskovic. Chromatic index of graphs with no cycle with unique chord . In: Proc. of the ALIO/EUROWorkshop on Applied Optimization (2008). Full paper submitted to Theoret. Comput. Sci.]: if the maximum degree is 3, the edge-colouring is NP-complete, otherwise, the problem is polynomial. Subsequently, Machado and Figueiredo [R. C. S. Machado and C. M. H. de Figueiredo. Total chromatic number of chordless graphs . In: Proc. of the Cologne-Twente Workshop (2009). Full paper submitted to Discrete Appl. Math.] settled the validity of the Total-Colouring Conjecture for {square,unichord}-free graphs by proving that non-complete {square,unichord}-free graphs of maximum degree at least 4 are Type 1. In the present work, we prove that non-complete {square,unichord}-free graphs of maximum degree 3 are Type 1, establishing the polynomiality of total-colouring restricted to {square,unichord}-free graphs.

Covert Attacks in Cyber-Physical Control Systems

The advantages of using communication networks to interconnect controllers and physical plants motivate the increasing number of networked control systems in industrial and critical infrastructure facilities. However, this integration also exposes such control systems to new threats, typical of the cyber domain. In this context, studies have been conducted, aiming to explore vulnerabilities and propose security solutions for cyber-physical systems. In this paper, a covert attack for service degradation is proposed, which is planned based on the intelligence gathered by another attack, herein proposed, referred as system identification attack. The simulation results demonstrate that the joint operation of the two attacks is capable to affect, in a covert and accurate way, the physical behavior of a system.

Biclique-colouring verification complexity and biclique-colouring power graphs

Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is co NP -complete to check whether a given function that associates a colour to each vertex is a biclique-colouring, a result that justifies the search for structured classes where the biclique-colouring problem could be efficiently solved. We consider biclique-colouring restricted to powers of paths and powers of cycles. We determine the biclique-chromatic number of powers of paths and powers of cycles. The biclique-chromatic number of a power of a path P n k is max ( 2 k + 2 - n , 2 ) if n ? k + 1 and exactly n otherwise. The biclique-chromatic number of a power of a cycle C n k is at most?3 if n ? 2 k + 2 and exactly n otherwise; we additionally determine the powers of cycles that are 2-biclique-colourable. All proofs are algorithmic and provide polynomial-time biclique-colouring algorithms for graphs in the investigated classes.

Software Analysis and Protection for Smart Metering

Abstract: Smart meters are devices equipped with embedded software that are capable of processing complex digital data. These devices are now a reality in most areas of metrology. They enable a number of new applications, but they also introduce new challenges with regards to their validation. This paper describes initiatives developed by Inmetro, the national metrology institute of Brazil, and Eletrobrás, a Brazilian power utility company, that are designed to support the validation of smart electricity meters.

On the embedding of cone graphs in the line with distinct distances between neighbors

Abstract A graph G = ( V , E ) is graceful if its vertices can be embedded in the interval [ 0 , | E | ] in such a way that: (1) all vertices have integer coordinates; (2) no two vertices share the same coordinate; and (3) the distances in the line between two adjacent vertices in the graph are all distinct. We show that the generalized cone graph C p + I q (the join of a cycle and an independent set) is graceful for p ∈ { 9 , 13 , 17 } and q ≥ 1 . We also show that C p + I q is not graceful for several odd values of q with p ≡ 2 ( mod 4 ) , disproving a conjecture of Brundage. Our results suggest a conjecture towards the characterization of graceful generalized cone graphs.

Using SPQR-trees to speed up recognition algorithms based on 2-cutsets ☆

Abstract Several well-studied classes of graphs admit structural characterizations via proper 2-cutsets which lead to polynomial-time recognition algorithms. The algorithms so far obtained for those recognition problems do not guarantee linear-time complexity. The bottleneck to those algorithms is the Ω ( n m ) -time complexity to fully decompose by proper 2-cutsets a graph with n vertices and m edges. In the present work, we investigate the 3-connected components of a graph and propose the use of the SPQR-tree data structure to obtain a fully decomposed graph in linear time. As a consequence, we show that the recognition of chordless graphs and of graphs that do not contain a propeller as a subgraph can be done in linear time, answering questions in the existing literature.

Using SPQR-trees to speed up algorithms based on 2-cutset decompositions

Abstract We propose the use of SPQR-trees as a data structure to encode the 3-connected components of a graph and to obtain linear-time recognition algorithms for graph classes structurally characterized by 2-cutset decompositions.

Metrologia Temporal na Verificação de Integridade de Software em Instrumentos de Medição

Este artigo descreve uma metodologia de verificacao da integridade de software apoiada na medicao de “efeitos colaterais”, eventos fisicos associados ao processamento de dados. Mostramos que a “metrologia de efeitos colaterais” aumenta a confianca no processo de verificacao de integridade. Apresentamos duas abordagens para uso de metrologia temporal em verificacao de integridade. A primeira abordagem permite a avaliacao do comportamento temporal de um software sem que seja necessario interromper o funcionamento do equipamento onde o software em verificacao esta embarcado. Na segunda abordagem, o funcionamento do equipamento deve ser interrompido e os modulos que armazenam o software em verificacao devem ser removidos, de forma a obter maior certeza acerca dos resultados obtidos.