An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Average complexity of a gift-wrapping algorithm for determining the convex hull of randomly given points

This paper presents an algorithm and its probabilistic analysis for constructing the convex hull of m given points in R"n, the n-dimensional Euclidean space. The algorithm under consideration combines the Gift-Wrapping-concept with the so-called Throw-Away-Principle for nonextremal points. In this paper the Simplex-Method is used to organize a walk over the surface of the convex hull. During this walk all facets are discovered. Under the condition of general position this information is sufficient, because the whole face-lattice can simply be deduced when the set of facets is availableSIGLEAvailable from TIB Hannover: RO 7722(478) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Effects of limestone calcination on the gasification processes in a BFB coal gasifier

An Eulerian-Eulerian computational fluid dynamics (CFD) model of the gasification processes in a coal bubbling fluidised bed (BFB) is presented incorporating the devolatilisation, heterogeneous, homogeneous reactions and limestone calcination. The model considers separate phases for the coal, limestone and char and is carried out for different experimental conditions taken from the literature.The results of the exiting gas compositions have been averaged over time and validated with experimental data. The hydrodynamic behaviour as well as temperature and reaction distributions within the bed are presented. The impact of limestone calcination on the gaseous composition is observe

Verbesserungen in der Laufzeitanalyse des Simplexverfahrens

Available from TIB Hannover: RO 7722(419) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Computing the convex hull in the Euclidean plane in linear expected time

SIGLETIB Hannover: RO 7722(139) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Empirical studies on the average efficiency of simplex-variants under rotation-symmetry

SIGLEAvailable from TIB Hannover: RO 7722(240) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman