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Fri, 30 Aug 2013 14:02:03 +0200Fri, 30 Aug 2013 14:02:03 +0200HUHFA: A Framework for Facet Classification
https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/4223
Usually complete linear descriptions of polytopes consist of
an enormous number of facet-defining inequalities already
for very small problem sizes. In this paper, we describe a method
for dividing the inequalities into equivalence classes without resorting to a normal form. Within each
class, facets are related by certain symmetries and it is sufficient
to list one representative of each class to give a complete
picture of the structural properties of a polytope. We propose an algorithm
for the classification and illustrate its efficiency on a broad range of combinatorial optimization problems including the Traveling Salesman and the Linear Ordering Problem.Olga Heismann; Achim Hildenbrandt; Francesco Silvestri; Gerhard Reinelt; Ralf BorndÃ¶rferreportzibhttps://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/4223Fri, 30 Aug 2013 14:02:03 +0200The Symbolic Integration of Exact PDEs
https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/570
An algorithm is described to decide if a given polynomial differential expression $\Delta$ of multivariate functions is exact, i.e. whether there exists a first integral $P$ such that $D_xP = \Delta$ for any one of a set of variables $x$ and to provide the integral $P$. A generalization is given to allow integration in the case that the exactness is prohibited by terms which contain only functions of not all the independent variables.Thomas Wolfreportzibhttps://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/570Mon, 31 Jan 2000 00:00:00 +0100