scholarly journals Group Degree Centrality and Centralization in Networks

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1810
Author(s):  
Matjaž Krnc ◽  
Riste Škrekovski
Keyword(s):  
Data Structure ◽  
Approximation Algorithm ◽  
Linear Time ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Central Group ◽  
Fast Running ◽  
Or Groups ◽  
Optimal Value ◽  
The One

The importance of individuals and groups in networks is modeled by various centrality measures. Additionally, Freeman’s centralization is a way to normalize any given centrality or group centrality measure, which enables us to compare individuals or groups from different networks. In this paper, we focus on degree-based measures of group centrality and centralization. We address the following related questions: For a fixed k, which k-subset S of members of G represents the most central group? Among all possible values of k, which is the one for which the corresponding set S is most central? How can we efficiently compute both k and S? To answer these questions, we relate with the well-studied areas of domination and set covers. Using this, we first observe that determining S from the first question is NP-hard. Then, we describe a greedy approximation algorithm which computes centrality values over all group sizes k from 1 to n in linear time, and achieve a group degree centrality value of at least (1−1/e)(w*−k), compared to the optimal value of w*. To achieve fast running time, we design a special data structure based on the related directed graph, which we believe is of independent interest.

scholarly journals Fast Fréchet Distance Between Curves with Long Edges

2019 ◽  
Vol 29 (02) ◽  
pp. 161-187
Author(s):  
Joachim Gudmundsson ◽  
Majid Mirzanezhad ◽  
Ali Mohades ◽  
Carola Wenk
Keyword(s):  
Data Structure ◽  
Approximation Algorithm ◽  
Special Class ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Fréchet Distance ◽  
Frechet Distance ◽  
Polygonal Curves

Computing the Fréchet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fréchet distance computations become easier. Let [Formula: see text] and [Formula: see text] be two polygonal curves in [Formula: see text] with [Formula: see text] and [Formula: see text] vertices, respectively. We prove four results for the case when all edges of both curves are long compared to the Fréchet distance between them: (1) a linear-time algorithm for deciding the Fréchet distance between two curves, (2) an algorithm that computes the Fréchet distance in [Formula: see text] time, (3) a linear-time [Formula: see text]-approximation algorithm, and (4) a data structure that supports [Formula: see text]-time decision queries, where [Formula: see text] is the number of vertices of the query curve and [Formula: see text] the number of vertices of the preprocessed curve.

A Hybrid Numerical Framework for Simulation of Ships Maneuvering in Waves

2021 ◽  
pp. 1-13
Author(s):  
Paul F. White ◽  
Dominic J. Piro ◽  
Bradford G. Knight ◽  
Kevin J. Maki
Keyword(s):  
Hydrodynamic Force ◽  
Linear Time ◽  
Domain Boundary ◽  
Critical Role ◽  
Force Model ◽  
Efficient Computation ◽  
Fast Running ◽  
Surface Ship ◽  
Calm Water ◽  
Maneuvering In Waves

The maneuvering characteristics of a surface ship play a critical role in the safety of navigation both in port and in an open seaway, and are vital to the overall operational ability of the ship. The vast majority of maneuvering analyses for ships have been performed under the assumption of calm water, yet ships mostly operate in waves. Understanding of maneuvering in waves is limited by the complexity of the problem and the challenges of performing physical experiments and numerical simulations. In this work, a new fast-running method that allows for the study of maneuvering in waves is formulated. The newly formulated approach is categorized as a “hybrid method,” taking its name from the multiple numerical methods and force models used to predict the total hydrodynamic force acting on the vessel maneuvering in waves. The framework presented here uses a combination of Computational Fluid Dynamics, a linear time-domain boundary element method, and a propeller-force model for efficient computation of the total hydrodynamic force.

scholarly journals A COMPARISON OF CENTRALITY MEASURES IN SUSTAINABLE DEVELOPMENT GOALS

2020 ◽  
Vol 14 (3) ◽  
pp. 309-320
Author(s):  
Sena Ariesandy ◽  
Ema Carnia ◽  
Herlina Napitupulu
Keyword(s):  
Sustainable Development ◽  
Millennium Development Goals ◽  
Sustainable Development Goals ◽  
Closeness Centrality ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Global Problems ◽  
Calculation Results ◽  
Development Goals

The Millennium Development Goals (MDGs), which began in 2000 with 8 goal points, have not been able to solve the global problems. The MDGs were developed into Sustainable Development Goals (SDGs) in 2015 with 17 targeted goal points achieved in 2030. Until now, methods for determining the priority of SDGs are still attractive to researchers. Centrality is one of the tools in determining the priority goal points on a network by using graph theory. There are four measurements of centrality used in this paper, namely degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. The calculation results obtained from the four measurements are compared, analyzed, to conclud which goal points are the most prior and the least prior. From the results obtained the most priority goal points in Sustainable Development Goals.

7 Conclusion

2020 ◽  
Author(s):  
De Wet Erika
Keyword(s):  
United Nations Security Council ◽  
West African ◽  
Military Assistance ◽  
Collective Security ◽  
Customary International Law ◽  
Or Groups ◽  
Peace And Security ◽  
Ambivalent Relationship ◽  
The One ◽  
The Cold War

This concluding chapter identifies what the customary international law requirements are for valid requests for military assistance. It also addresses the ambivalent relationship between this legal construct and the notion of collective security embodied in the UN Charter. On the one hand, there is the risk that military assistance provided by individual states or groups of states undermines the notion of the centralization of decisions regarding the use of force with the United Nations Security Council. It can further perpetuate the perception of neo-colonialism and imperialism that have been associated with military assistance on request ever since the Cold War. On the other hand, clauses such as article 4(j) and potentially article 4(h) of the African Union Constitutive Act and article 25 of the Economic Community of West African States Mechanism Protocol suggest that military assistance on request can be deployed as a mechanism for maintaining regional peace and security. This suggests that, depending on the context, military assistance on request can be utilized in the interests of international peace and security and could therefore be reconcilable with the notion of collective security underpinning the UN Charter.

Graph matching

2020 ◽  
pp. 291-358
Author(s):  
Rob H. Bisseling
Keyword(s):  
Approximation Algorithm ◽  
Parallel Algorithm ◽  
Graph Matching ◽  
Linear Time ◽  
Total Weight ◽  
Mathematical Representation ◽  
Optimal Weight ◽  
Graph Problems ◽  
Positive Weights ◽  
Local Dominance

This chapter explores parallel algorithms for graph matching. Here, a graph is the mathematical representation of a network, with vertices representing the nodes of the network and edges representing their connections. The edges have positive weights, and the aim is to find a matching with maximum total weight. The chapter first presents a sequential, parallelizable approximation algorithm based on local dominance that guarantees attaining at least half the optimal weight in near-linear time. This algorithm, coupled with a vertex partitioning, is the basis for developing a parallel algorithm. The BSP approach is shown to be especially advantageous for graph problems, both in developing a parallel algorithm and in proving it correct. The basic parallel algorithm is enhanced by giving preference to local matches when breaking ties and by adding a load-balancing mechanism. The scalability of the parallel algorithm is put to the test using graphs of up to 150 million edges.

Law, Religion, and the Present Danger

Worldview ◽  
1979 ◽  
Vol 22 (9) ◽  
pp. 46-53
Author(s):  
Harold J. Berman
Keyword(s):  
First Amendment ◽  
The United States ◽  
United States Constitution ◽  
Establishment Clause ◽  
Free Exercise ◽  
Group Activities ◽  
Or Groups ◽  
Governmental Support ◽  
The One ◽  
Governmental Control

When the word "law" is juxtaposed with the word "religion," an American lawyer today is apt to think immediately of the First Amendment to the United States Constitution with its double protection against any governmental interference in "the free exercise" of religion on the one hand and against any governmental "establishment" of religion on the other. From the standpoint of contemporary American constitutional law, religion has become the personal and private affair of individual citizens or groups of citizens. Indeed, in recent decades our courts, in interpreting the "free exercise" clause, have gone far toward immunizing individual and group activities from governmental control, whether federal or state, whenever they are considered by the persons engaging in them to be of a religious character; and at the same time, under the "establishment" clause the courts have struck down most forms even of indirect governmental support of religion, whether federal or state.

scholarly journals A generalized Robinson-Foulds distance for labeled trees

BMC Genomics ◽  
2020 ◽  
Vol 21 (S10) ◽  
Author(s):  
Samuel Briand ◽  
Christophe Dessimoz ◽  
Nadia El-Mabrouk ◽  
Manuel Lafond ◽  
Gabriela Lobinska
Keyword(s):  
Approximation Algorithm ◽  
Phylogenetic Trees ◽  
Linear Time ◽  
Crucial Aspect ◽  
Labeled Trees ◽  
Link Type

Abstract Background The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). Results We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting “good” edges, i.e. edges shared between the two trees. Conclusions We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions.Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf.

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