28,177 research outputs found
Protecting a Graph with Mobile Guards
Mobile guards on the vertices of a graph are used to defend it against
attacks on either its vertices or its edges. Various models for this problem
have been proposed. In this survey we describe a number of these models with
particular attention to the case when the attack sequence is infinitely long
and the guards must induce some particular configuration before each attack,
such as a dominating set or a vertex cover. Results from the literature
concerning the number of guards needed to successfully defend a graph in each
of these problems are surveyed.Comment: 29 pages, two figures, surve
Disjoint Dominating Sets with a Perfect Matching
In this paper, we consider dominating sets and such that and
are disjoint and there exists a perfect matching between them. Let
denote the cardinality of smallest such sets in
(provided they exist, otherwise ). This
concept was introduced in [Klostermeyer et al., Theory and Application of
Graphs, 2017] in the context of studying a certain graph protection problem. We
characterize the trees for which equals a certain
graph protection parameter and for which ,
where is the independence number of . We also further study this
parameter in graph products, e.g., by giving bounds for grid graphs, and in
graphs of small independence number
Guarding Networks Through Heterogeneous Mobile Guards
In this article, the issue of guarding multi-agent systems against a sequence
of intruder attacks through mobile heterogeneous guards (guards with different
ranges) is discussed. The article makes use of graph theoretic abstractions of
such systems in which agents are the nodes of a graph and edges represent
interconnections between agents. Guards represent specialized mobile agents on
specific nodes with capabilities to successfully detect and respond to an
attack within their guarding range. Using this abstraction, the article
addresses the problem in the context of eternal security problem in graphs.
Eternal security refers to securing all the nodes in a graph against an
infinite sequence of intruder attacks by a certain minimum number of guards.
This paper makes use of heterogeneous guards and addresses all the components
of the eternal security problem including the number of guards, their
deployment and movement strategies. In the proposed solution, a graph is
decomposed into clusters and a guard with appropriate range is then assigned to
each cluster. These guards ensure that all nodes within their corresponding
cluster are being protected at all times, thereby achieving the eternal
security in the graph.Comment: American Control Conference, Chicago, IL, 201
Unusual Features of Varying Speed of Light Cosmologies
We contrast features of simple varying speed of light (VSL) cosmologies with
inflationary universe models. We present new features of VSL cosmologies and
show that they face problems explaining the cosmological isotropy problem. We
also find that if c falls fast enough to solve the flatness and horizon
problems then the quantum wavelengths of massive particle states and the radii
of primordial black holes can grow to exceed the scale of the particle horizon.
This may provide VSL cosmologies with a self-reproduction property. The
constraint of entropy increase is also discussed. The new problems described in
the this letter provide a set of bench tests for more sophisticated VSL
theories to pass.Comment: expanded version, 12 page
Cosmology without inflation
We propose a new cosmological paradigm in which our observed expanding phase
is originated from an initially large contracting Universe that subsequently
experienced a bounce. This category of models, being geodesically complete, is
non-singular and horizon-free, and can be made to prevent any relevant scale to
ever have been smaller than the Planck length. In this scenario, one can find
new ways to solve the standard cosmological puzzles. One can also obtain scale
invariant spectra for both scalar and tensor perturbations: this will be the
case, for instance, if the contracting Universe is dust-dominated at the time
at which large wavelength perturbations get larger than the curvature scale. We
present a particular example based on a dust fluid classically contracting
model, where a bounce occurs due to quantum effects, in which these features
are explicit.Comment: 8 pages, no figur
Um problema de dominação eterna : classes de grafos, métodos de resolução e perspectiva prática
Orientadores: Cid Carvalho de Souza, Orlando LeeTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O problema do conjunto dominante m-eterno é um problema de otimização em grafos que tem sido muito estudado nos últimos anos e para o qual se têm listado aplicações em vários domínios. O objetivo é determinar o número mínimo de guardas que consigam defender eternamente ataques nos vértices de um grafo; denominamos este número o índice de dominação m-eterna do grafo. Nesta tese, estudamos o problema do conjunto dominante
m-eterno: lidamos com aspectos de natureza teórica e prática e abordamos o problema
restrito a classes especícas de grafos e no caso geral. Examinamos o problema do conjunto dominante m-eterno com respeito a duas classes de grafos: os grafos de Cayley e os conhecidos grafos de intervalo próprios. Primeiramente, mostramos ser inválido um resultado sobre os grafos de Cayley presente na literatura, provamos que o resultado é válido para uma subclasse destes grafos e apresentamos outros achados. Em segundo lugar, fazemos descobertas em relação aos grafos de intervalo próprios, incluindo que, para estes grafos, o índice de dominação m-eterna é igual à cardinalidade máxima de um conjunto independente e, por consequência, o índice de dominação m-eterna pode ser computado em tempo linear.
Tratamos de uma questão que é fundamental para aplicações práticas do problema do
conjunto dominante m-eterno, mas que tem recebido relativamente pouca atenção. Para
tanto, introduzimos dois métodos heurísticos, nos quais formulamos e resolvemos modelos
de programação inteira e por restrições para computar limitantes ao índice de dominação
m-eterna. Realizamos um vasto experimento para analisar o desempenho destes métodos.
Neste processo, geramos um benchmark contendo 750 instâncias e efetuamos uma
avaliação prática de limitantes ao índice de dominação m-eterna disponíveis na literatura.
Por m, propomos e implementamos um algoritmo exato para o problema do conjunto
dominante m-eterno e contribuímos para o entendimento da sua complexidade: provamos
que a versão de decisão do problema é NP-difícil. Pelo que temos conhecimento, o algoritmo
proposto foi o primeiro método exato a ser desenvolvido e implementado para o
problema do conjunto dominante m-eternoAbstract: The m-eternal dominating set problem is a graph-protection optimization problem that has been an active research topic in the recent years and reported to have applications in various domains. It asks for the minimum number of guards that can eternally defend attacks on the vertices of a graph; this number is called the m-eternal domination number of the graph. In this thesis, we study the m-eternal dominating set problem by dealing with aspects of theoretical and practical nature and tackling the problem restricted to specic classes of graphs and in the general case. We examine the m-eternal dominating set problem for two classes of graphs: Cayley graphs and the well-known proper interval graphs. First, we disprove a published result on the m-eternal domination number of Cayley graphs, show that the result is valid for a subclass of these graphs, and report further ndings. Secondly, we present several discoveries regarding proper interval graphs, including that, for these graphs, the m- eternal domination number equals the maximum size of an independent set and, as a consequence, the m-eternal domination number can be computed in linear time. We address an issue that is fundamental to practical applications of the m-eternal dominating set problem but that has received relatively little attention. To this end, we introduce two heuristic methods, in which we propose and solve integer and constraint programming models to compute bounds on the m-eternal domination number. By performing an extensive experiment to validate the features of these methods, we generate a 750-instance benchmark and carry out a practical evaluation of bounds for the m-eternal domination number available in the literature. Finally, we propose and implement an exact algorithm for the m-eternal dominating set problem and contribute to the knowledge on its complexity: we prove that the decision version of the problem is NP-hard. As far as we know, the proposed algorithm was the first developed and implemented exact method for the m-eternal dominating set problemDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação141964/2013-8CAPESCNP
An Eternal Domination Problem in Grids
A dynamic domination problem in graphs is considered in which an infinite sequence of attacks occur at vertices with mobile guards; the guard at the attacked vertex is required to vacate the vertex by moving to a neighboring vertex with no guard. Other guards are allowed to move at the same time, and before and after each attack, the vertices containing guards must form a dominating set of the graph. The minimum number of guards that can defend the graph against such an arbitrary sequence of attacks is called the m-eviction number of the graph. In this paper, the m-eviction number is determined exactly for grids with and upper bounds are given for all
- …