Open k-monopolies in graphs: complexity and related concepts

Closed monopolies in graphs have a quite long range of applications in several problems related to overcoming failures, since they frequently have some common approaches around the notion of majorities, for instance to consensus problems, diagnosis problems or voting systems. We introduce here open $k$-monopolies in graphs which are closely related to different parameters in graphs. Given a graph $G=(V,E)$ and $X\subseteq V$, if $\delta_X(v)$ is the number of neighbors $v$ has in $X$, $k$ is an integer and $t$ is a positive integer, then we establish in this article a connection between the following three concepts: - Given a nonempty set $M\subseteq V$ a vertex $v$ of $G$ is said to be $k$-controlled by $M$ if $\delta_M(v)\ge \frac{\delta_V(v)}{2}+k$. The set $M$ is called an open $k$-monopoly for $G$ if it $k$-controls every vertex $v$ of $G$. - A function $f: V\rightarrow \{-1,1\}$ is called a signed total $t$-dominating function for $G$ if $f(N(v))=\sum_{v\in N(v)}f(v)\geq t$ for all $v\in V$. - A nonempty set $S\subseteq V$ is a global (defensive and offensive) $k$-alliance in $G$ if $\delta_S(v)\ge \delta_{V-S}(v)+k$ holds for every $v\in V$. In this article we prove that the problem of computing the minimum cardinality of an open $0$-monopoly in a graph is NP-complete even restricted to bipartite or chordal graphs. In addition we present some general bounds for the minimum cardinality of open $k$-monopolies and we derive some exact values.Comment: 18 pages, Discrete Mathematics & Theoretical Computer Science (2016

A Survey on Alliances and Related Parameters in Graphs

In this paper, we show that several graph parameters are known in different areas under completely different names.More specifically, our observations connect signed domination, monopolies, $\alpha$-domination, $\alpha$-independence,positive influence domination,and a parameter associated to fast information propagationin networks to parameters related to various notions of global $r$-alliances in graphs.We also propose a new framework, called (global) $(D,O)$-alliances, not only in order to characterizevarious known variants of alliance and domination parameters, but also to suggest a unifying framework for the study of alliances and domination.Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations

On the approximability and exact algorithms for vector domination and related problems in graphs

We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in S. In total vector domination, the requirement is extended to all vertices of the graph. We prove that these problems (and several variants thereof) cannot be approximated to within a factor of clnn, where c is a suitable constant and n is the number of the vertices, unless P = NP. We also show that two natural greedy strategies have approximation factors ln D+O(1), where D is the maximum degree of the input graph. We also provide exact polynomial time algorithms for several classes of graphs. Our results extend, improve, and unify several results previously known in the literature.Comment: In the version published in DAM, weaker lower bounds for vector domination and total vector domination were stated. Being these problems generalization of domination and total domination, the lower bounds of 0.2267 ln n and (1-epsilon) ln n clearly hold for both problems, unless P = NP or NP \subseteq DTIME(n^{O(log log n)}), respectively. The claims are corrected in the present versio

The complexity of open k-monopolies in graphs for negative k

Let $G$ be a graph with vertex set $V(G)$, $\delta(G)$ minimum degree of $G$ and $k\in\left\{1-\left\lceil\frac{\delta(G)}{2}\right\rceil,\ldots ,\left\lfloor \frac{\delta(G)}{2}\right\rfloor\right\}$. Given a nonempty set $M\subseteq V(G)$ a vertex $v$ of $G$ is said to be $k$-controlled by $M$ if $\delta_M(v)\ge\frac{\delta_{V(G)}(v)}{2}+k$ where $\delta_M(v)$ represents the number of neighbors of $v$ in $M$. The set $M$ is called an open $k$-monopoly for $G$ if it $k$-controls every vertex $v$ of $G$. In this short note we prove that the problem of computing the minimum cardinality of an open $k$-monopoly in a graph for a negative integer $k$ is NP-complete even restricted to chordal graphs

The Application of EC Competition Policy to the Media Industry

This article examines whether EC competition policy and merger control provisions can prevent excessive market power and safeguard open access and consumer choice in the European media and communications industry. The study looks at the structure of the media industry and points to the amalgamation of corporate power. It assesses whether EC competition law and merger provisions can effectively address the dangers of ownership concentration and safeguard diversity of sources. A number of merger cases either blocked or allowed by the EC are reviewed in order to establish the level of competition. The article suggests that a more rigorous competition policy is required to guarantee competition and prevent domination in merger activity

Experimentation and innovation in police reform: Timor-Leste, Solomon Islands and Bougainville

The plural character of policing provision in most countries is now widely acknowledged, though rarely reflected in the practical police reform programming undertaken by donors. While much of the literature on international police assistance focuses on its modest results and innate limitations, less attention has been paid to those still relatively rare programmes that have sought to engage with the local realities of plural policing. This is particularly so in the conflict-affected and fragile settings where such assistance is typically provided. In this article, we present three case studies of policing innovation and experimentation from Timor-Leste, Solomon Islands and Bougainville, respectively, set in the context of the recent and very different post-conflict interventions in each place. While not wishing to overstate the impact of these modest programmes, we highlight their potential contribution to fostering productive relations across the multiple social orders and sources of authority found in many post-colonial, post-conflict and otherwise fragile contexts. We tentatively conclude that the most significant contribution of these kinds of initiative is likely to lie beyond the realm of institutionalised policing and, specifically, in relation to larger processes of social and political change, including state formation, under way in these places

Privatization and management accounting systems change : the case of the 19th century Spanish tobacco monopoly.

This paper examines changes to the accounting system of the Spanish tobacco monopoly in 1887, following the decision by the state to lease the publicly owned and state-run monopoly to a privatesector company. The switch to private-sector management generated a fundamental change in the demands made of the accounting system. As a result, double-entry bookkeeping and a new method of calculating costs were implemented. The paper discusses the motives behind the design of the new accounting system and its consequences using the framework provided by agency theory. It highlights the need to consider the role of the capital structure of the firm and the state as explanatory factors for both the parameters and uses of cost accounting information.Privatización; Monopolio; Tabaco; España; S. XIX;

Securing the state, undermining democracy: internationalization and privatization of western militaries

Changes in the field of security since the 1990s triggered off a number of still continuing military transformations in liberal democracies. Since their armed forces were designed for the purposes of the bipolar Cold war security constellation, they have been “redesigned” according to the new tasks as agreed upon in the new NATO strategic concepts or the assignments for the Europeanized forces within the European Union: Conflict prevention, crisis intervention, counter-terrorism have been added to the range of deployment missions. This recent transformation of the armed forces is pushed ahead in the political spirit of new public management well known from other policy areas in the OECD countries. The proclaimed reforms are guided by efficiency and effectiveness principles only, issues of democratic control and integration of the armed forces into the society are marginalized in the political discourse. But integration and cooperation within international organizations is only one of the two trends detrimental to democratic control of the military; increasing contracting with Private Security and Military Companies is the other. Contracting is intended to reduce political and financial costs and risks for Western governments. The authors argue that, in the long run, both trends of privatization and internationalization, though they seem to run into opposite directions from a purely etatist perspective, result in the joint effect of exacerbating democratic control and accountability of security policies. This point is illustrated by the employment of private military companies by the US government agencies and US military and the reform of the German armed forces. -- Seit Ende des Ost-West-Konflikts befinden sich die westlichen Streitkräfte in einem anhaltenden Transformationsprozess. Waren die Streitkräfte zuvor an der bipolaren Sicherheitskonstellation des Kalten Krieges ausgerichtet, werden sie seit 1990 umstrukturiert, um neue Missionen zu erfüllen, wie sie in den strategischen Konzepten der NATO oder den Aufgabenfeldern der Europäischen Sicherheits- und Verteidigungspolitik definiert sind. Unter den Vorzeichen eines New Public Managements vorangetrieben, das in den letzten Jahrzehnten als ökonomisch inspiriertes Reformprinzip bereits zahlreiche andere Politikfelder der OECD-Staaten geprägt hat, sind die Umstrukturierungen der Streitkräfte vorwiegend an Effizienz- und Effektivitäts-Gesichtspunkten orientiert. Fragen der demokratischen Kontrolle und der Integration des Militärs in die jeweilige Gesellschaft werden dagegen im politischen Diskurs vernachlässigt. Zwei Entwicklungstrends kennzeichnen derzeit die westliche Sicherheits- und Verteidigungspolitik: die Integration und Kooperation westlicher Streitkräfte im Rahmen von internationalen Organisationen sowie der zunehmende Einsatz privater Sicherheitsunternehmen. Obwohl Internationalisierung und Privatisierung von Sicherheitspolitik in einer staatszentrierten Perspektive auf den ersten Blick gegenläufige Tendenzen einer Stärkung der Exekutive einerseits und der Schwächung des Staates andererseits zu markieren scheinen, tragen jedoch beide zu einer Schädigung der nationalstaatlichen Demokratie bei. Diese These erläutern die Autorinnen anhand des vermehrten Rückgriffs der US-amerikanischen Regierung auf private Sicherheitsanbieter sowie der Transformation der deutschen Streitkräfte.