Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

The quality of political news in a changing media environment

What do ongoing changes in the media environment, notably the perceived popularization of news and the shift towards individualized online media, mean for political news quality, both in terms of what it is, as well as how we measure it? This dissertation firstly argues, based on a literature review showing the benefits and risks of popular and online news for democracy, that news quality standards should be more lenient towards popular news elements. These elements, such as relatively low complexity, a focus on leaders and a more emotional style, may increase political interest and knowledge among specific audience groups. In the online environment characterized by information overload and vulnerable to bias as a consequence of audience preference tracking, drawing people’s attention and keeping it is arguably just as important as transmitting political information. Secondly, a content analysis of political news in Austrian online and print newspapers during the 2013 election campaign shows that in print, elite and popular newspapers perform rather similar across quality indicators, including content complexity. However, online, popular newspapers perform worse, even if we emphasize involvement alongside information. Lastly, the dissertation discusses automatic content analysis methods, and demonstrates the use of topic modelling, and inductive method for exploring themes in the news. Although allowing the analysis of larger data sets, automatic content analysis is still limited in the news quality indicators it can measure. Further research should refine existing methods for communication studies goals, and find ways to effectively combine automatic and human coding