Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs

The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. Similarly, greedy algorithms deliver very good approximations to the optimal solution in practice. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that, on real instances, this leads to better approximations than the standard greedy approach within reasonable time

Aesthetics of the anthropocene : an analysis of german rap’s critique on the surveillance system of time

Post-modernity is thought of as an era of contradictions. Mass media, the Web 3.0, and cor-porate governance cause an increasing level of insecurity regarding the validity of infor-mation. Furthermore, liberty is renamed into freedom to legitimize polluting and exploitive actions which appear altogether grounded on managerial interests. In Marcusian thought, this dissertation contributes to the function of the arts as means of knowledge production, while focusing on German rap as one of the most consumed forms of post-modern popular culture. The work at hand argues that to keep society under control, the metaphysical element of time has been gradually turned into a tool of surveillance. Drawing on Kutschera’s con-cept of aesthetics, a critical, textual analysis of eight contemporary German rap lyrics is conducted. The two-sided argumentation firstly focuses on a vertical time axis of post-in-dustrial society, in which time has become the object of a trade-off calculation between physical and digital control and one’s individual material wealth. The second part argues along a horizontal time axis. Physical control mechanisms have been in place since the days of imperialism, as the principles of colonialism moved through time and space to secure the current hegemony of Western nation-states. Hence, climate change and the refugee move-ments were caused and are fostered. The dissertation closes with a change of perspective, which is achieved through two affirmative rap lyrics. In turn, possible lines of further re-search are generated

E-fuels and climate goals : an analysis of the German automotive industry

Climate change is increasingly impacting life globally. To reduce damage, stricter governmental regulations have been developed, and companies need to adapt to these changes. The automotive industry is transitioning towards new technologies like electrification or hybrid systems to comply with these regulations. This study investigates how so called “e-fuels” could impact the automotive industry. E-fuels are an innovative alternative to fossil fuels, compatible with a combustion car fleet and can be produced in a CO2 neutral manner. Experts from different areas related to the automotive industry in Germany were interviewed. The potential of e-fuels was evaluated and the importance of an ambidextrous strategy was discussed. Synthesizing the experts’ opinions gives two key problems for e-fuels: Energy efficiency and the lack of accreditation in the current European regulation. A global value chain and technology openness could help to overcome these problems. The potential for e-fuels therefore depends on regulation and is significantly reduced by the current fleet emission regulation in Europe. In fields where no substitution with other technologies is possible, e-fuels will likely become a standard. Manufacturers will continue to sell combustion cars in the next decades, but the ambidextrous approach is restricted by regulations. The simultaneous development of electric and combustion technology is costly and unlikely for most car manufacturers. Thus, many will transition towards complete electrification. Further research should include experts from other related fields and regions beyond Europe to investigate the global potential of e-fuels.As alterações climáticas estão a ter um impacto a nível global. Foram desenvolvidas regulamentações governamentais mais rígidas e as empresas precisam se adaptar a essas mudanças. A indústria automotiva está em transição para novas tecnologias, como eletrificação ou sistemas híbridos. Este estudo investiga como os “e-combustíveis” podem impactar a indústria automotiva. Os e-combustíveis são uma alternativa inovadora aos combustíveis fósseis, compatíveis com carros de combustão e podem ser produzidos de forma neutra em CO2. Foram entrevistados especialistas da indústria automotiva na Alemanha. O potencial dos e-combustíveis foi avaliado e discutida a importância de uma estratégia ambidestra. Dois problemas fundamentais para os e-combustíveis resultaram: a eficiência energética e a falta de credenciamento na atual regulamentação europeia. Uma cadeia de valor global e abertura tecnológica podem ajudar. O potencial dos e-combustíveis depende da regulamentação e é significativamente reduzido pela atual regulamentação de emissões na Europa. Em setores onde a substituição por outras tecnologias não é possível, os e-combustíveis provavelmente se tornarão a norma. Os fabricantes continuarão a vender carros a combustão, mas a abordagem ambidestro é restringida por regulamentos. O desenvolvimento simultâneo de tecnologia elétrica e de combustão é caro e improvável para a maioria dos fabricantes. Muitos farão a transição para a eletrificação total. A pesquisa futura deve incluir especialistas de outros setores e regiões fora da Europa para investigar o potencial dos e-combustíveis

Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs

Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent beta, and high clustering that can be controlled via the temperature T. We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to T = 0. We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input. Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases

Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry

Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this tradeoff. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of ?2. On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we close the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a (1 + o(1))-approximation, asymptotically almost surely, and has a running time of ?(m log(n)). The proposed algorithm is an adaption of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the tradeoff between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach

The US Chapter 9 procedure: a plea for a useful model for solving excessive indebtedness of municipalities

Includes bibliographical referencesThis work is dedicated in the first instance to the necessity of insolvency proceedings for municipalities as territorial entities. Therefore, the current debate on insolvency proceedings for states is presented briefly in an introductory overview to introduce the debate that insolvency proceedings for territorial entities has reached all levels of government worldwide. This is followed by examples of historical experience with insolvency scenarios of states and local authorities to show that insolvency scenarios at all levels of government are part of reality, and that a procedural handling is possible, but also necessary. Based on this, the US-Chapter 9 procedure, perhaps the most well-known legal remedy for insolvent cities, and the most globally developed proceeding for municipal insolvencies, is taken closer into view. In the first step, the principles and mechanisms are pointed out. This is followed by a semantic preamble regarding the development of insolvency law and its public perception, a short discussion of the experience with the Chapter 9 process and last, but not least, a presentation of the key advantages of Chapter 9 proceedings. The goal is to convey that the Chapter 9 proceeding may serve as a useful tool and model for other countries to solve excessive indebtness of municipalities. As a result, in particular, the abstract possibilities and objectives of the procedure are considered

Total Hip Replacement in Developmental Dysplasia

Total hip arthroplasty (THA) for osteoarthritis secondary to development dysplasia of the hip (DDH) is facing increasing levels of complexity with increasing grade of deformity. The dysplastic acetabulum is characterized by diminished bone stock with decreased lateral coverage. Therefore, it is challenging to restore the anatomic center of rotation and ensure adequate acetabular component fixation. Surgical strategies include a medialization of the acetabular component, a higher hip center, lateral structural bone grafting and the selection of smaller component sizes to improve native bone coverage. Excessive femoral anteversion is commonly encountered in patients with developmental dysplasia. Moreover, the intramedullary canal is narrow and the neck often aligned in valgus. Modular implants are helpful to address the altered femoral anatomy and also facilitate femoral shortening osteotomies in patients with high hip dislocation. Although clinical results are comparable to primary total hip replacement in primary osteoarthritis, the risk for revision surgery due to dislocation and loosening is increased. The current chapter reviews classification, preoperative planning, and surgical strategies for patients undergoing THA for osteoarthritis secondary to developmental dysplasia

Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs

A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs

Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry

Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this trade-off. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of $\sqrt{2}$. On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we narrow the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a (1+(1))-approximation, asymptotically almost surely, and has a running time of ${\mathcal {O}}(m \log (n))$. The proposed algorithm is an adaptation of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the trade-off between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach