The impact of climate change to biosphere and the human civilization living therein are widely discussed as is the need to reduce the consumption of energy and materials – measured in footprints. Despite of that the means on how to reduce footprints and the difficulties going along with that are lesser discussed.The assessment of CO2 Footprints during all phases of its production and existence (Life Cycle Assessment) is embedded in the legally required of non-financial reporting for companies. This talk is intended to provide background on non-financial reporting and how that relates to footprints and risks. Of course reporting is not l´art pour l´art. It is intended to reduce the impact of an activity – Ecodesign and it impacts the value of companies. The intent is to discuss in more detail how reporting is done, how (CO2-) Footprints are derived, ways to reduce footprints and how the related activities influence the value of companies.

The edge expansion is an NP-hard to compute graph constant and gives us information about the connectivity of a graph. It is the minimum ratio of the number of edges joining two sets and the size of the smaller set over all possible non-trivial bipartitions of the vertices. The edge expansion of a connected graph is small if there is a bottleneck between two large parts of the graph. Because of this fact, it is for example used in clustering or network design. There are some heuristics to find a bipartition, like the well-known spectral clustering. This fractional optimization problem does not fit into the typical setting like other graph constants as the maximum cut which are NP-hard to compute. We propose different strategies to compute the edge expansion efficiently. One is to divide the problem into subproblems of an easier-to-handle type. Another one is to apply Dinkelbach's algorithm for fractional programming. Furthermore, we investigate the conjecture of Mihail and Vazirani, stating that the edge epxansion of the graph from a 0/1-polytope is at least 1, using our techniques.