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  • 68-XX COMPUTER SCIENCE (For papers involving machi...

68-04 Explicit machine computation and programs (not the theory of computation or programming)

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Author

  • Borndörfer, Ralf (1)
  • Heismann, Olga (1)
  • Hildenbrandt, Achim (1)
  • Reinelt, Gerhard (1)
  • Silvestri, Francesco (1)
  • Wolf, Thomas (1)

Year of publication

  • 2013 (1)
  • 2000 (1)

Keywords

  • facet classification (1)
  • partial differential equations (1)
  • polyhedral structure (1)
  • symbolic integration (1)
  • symmetry (1)

Institute

  • Mathematical Optimization (1)
  • ZIB Allgemein (1)

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HUHFA: A Framework for Facet Classification (2013)
Heismann, Olga ; Hildenbrandt, Achim ; Silvestri, Francesco ; Reinelt, Gerhard ; Borndörfer, Ralf
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.
The Symbolic Integration of Exact PDEs (2000)
Wolf, Thomas
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.
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