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In dem Bereich, in dem die in diesem Kapitel zu beschreibende Freiwilligenarbeit stattfindet – der hauslichen Sterbebegleitung –, ist die Einbindung der jeweiligen Personen von ganz anderer Natur als z. B. in der Jugendsportarbeit oder dem Voluntourismus. Palliative Care will Leiden lindern, den unheilbar kranken Mitmenschen in den Tod begleiten und dabei die Wurde der Person achten und auch Selbstbestimmung am Ende des Lebens ermoglichen. Dies gelingt nur, wenn – im Gegensatz zu vielen anderen Domanen der Freiwilligenarbeit – ein umfassendes und robustes Beziehungs- und Betreuungsnetz aufgebaut und meist im 24-Stunden-Rhythmus aufrecht erhalten und von daher intensiv koordiniert wird. In dieses Betreuungsnetz sind unterschiedliche Spezialisten und Fachpersonen, Angehorige, u. U. die Nachbarschaft und heute ganz selbstverstandlich auch Freiwillige eingebunden: jeder in seiner Rolle, keiner durch den anderen ersetzbar!

We define the class of geared (fuzzy) line graphsas the class of graphs obtained by repeated applications of the extended gear composition to a (fuzzy) line graph H. Using the decomposition theorem for claw-free graphs of Chudnovsky and Seymour [2], we show that this class represents a large subclass of claw-free graphs having stability number at least 4. We provide a complete linear description of the stable set polytope of geared (fuzzy) line graphs. This result gives a first substantial answer to the longstanding open question of finding a defining linear system for the stable set polytope of claw-free graphs [10].

Shifting bounds for on-line classification algorithms ensure good performance on any sequence of examples that is well predicted by a sequence of smoothly changing classifiers. When proving shifting bounds for kernel-based classifiers, one also faces the problem of storing a number of support vectors that can grow unboundedly, unless an eviction policy is used to keep this number under control. In this paper, we show that shifting and on-line learning on a budget can be combined surprisingly well. First, we introduce and analyze a shifting Perceptron algorithm achieving the best known shifting bounds while using an unlimited budget. Second, we show that by applying to the Perceptron algorithm the simplest possible eviction policy, which discards a random support vector each time a new one comes in, we achieve a shifting bound close to the one we obtained with no budget restrictions. More importantly, we show that our randomized algorithm strikes the optimal trade-off $U = \Theta\bigl(\sqrt{B}\bigr)$between budget B and norm U of the largest classifier in the comparison sequence.

We present a new "primal" algorithm for the stable set problem. It is based on a purely combinatorial construction that can transform every graph into a perfect graph by replacing nodes with sets of new nodes. The transformation is done in such a way that every stable set in the perfect graph corresponds to a stable set in the original graph. The algorithm keeps a formulation of the stable set problem in a simplex-type tableau whose associated basic feasible solution is the incidence vector of the best known stable set. The combinatorial graph transformations are performed by substitutions in the generators of the feasible region. Each substitution cuts off a fractional neighbor of the current basic feasible solution. We show that "dual-type" polynomial-time separation algorithms carry over to our "primal" setting. Eventually, either a nondegenerate pivot leading to an integral basic feasible solution is performed, or the optimality of the current solution is proved.