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When there are many people who don't need to expect something more than the benefits to take, we will suggest you to have willing to reach all benefits. Be sure and surely do to take this algorithms and data structures in vlsi design obdd foundations and applications that gives the best reasons to read. When you really need to get the reason why, this… (More)

Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on plane curves and linear spaces. New results include a complete description of the families of quadrics through four points in… (More)

- Ravi Kannan, Thorsten Theobald
- SODA
- 2007

We propose and investigate bimatrix games, whose (entry-wise) sum of the pay-off matrices of the two players is of rank <i>k</i>, where <i>k</i> is a constant. We will say the rank of such a game is <i>k</i>. For every fixed <i>k</i>, the class of rank <i>k</i>-games strictly generalizes the class of zero-sum games, but is a very special case of general… (More)

We provide a characterization of the radii minimal projections of polytopes onto j-dimensional subspaces in Euclidean space E. Applied on simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. In the second part… (More)

- Christoph Meinel, Thorsten Theobald
- Universität Trier, Mathematik/Informatik…
- 1996

Ordered binary decision diagrams are the state-of-the-art representation of switching functions. In order to keep the sizes of the OBDDs tractable, heuristics and dynamic reordering algorithms are applied to optimize the underlying variable order. When-nite state machines are represented by OBDDs the state encoding can be used as an additional optimization… (More)

- Christoph Meinel, Fabio Somenzi, Thorsten Theobald
- Universität Trier, Mathematik/Informatik…
- 1996

We propose a new algorithm, called linear sifting, for theoptimization of decision diagrams that combines the efficiency of sifting and the power of linear transformations. We show that the new algorithm is applicable to large examples, and that inmany cases it leads to substantiallymore compact diagrams when compared to simple variablereordering. We show… (More)

- Reinhard Steffens, Thorsten Theobald
- Comput. Geom.
- 2010

We use Bernstein’s Theorem [1] to obtain combinatorial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. The bounds can easily be computed and for some classes of graphs, the bounds are tight.

- Gábor Megyesi, Frank Sottile, Thorsten Theobald
- Discrete & Computational Geometry
- 2003

We solve the following geometric problem, which arises in several threedimensional applications in computational geometry: For which arrangements of two lines and two spheres in R are there infinitely many lines simultaneously transversal to the two lines and tangent to the two spheres? We also treat a generalization of this problem to projective quadrics:… (More)

- Christoph Meinel, Thorsten Theobald
- ITA
- 1997

Ordered binaxy décision diagrams are an important data structure for the représentation of Boolean functions. Typically, the underlying variable ordering is used as an optimization parameter. When finite state machines are represented by OBDDs the state encoding can be used as an additional optimization parameter. In this paper, we analyze the influence of… (More)

- Kerstin Hept, Thorsten Theobald
- 2007

We consider the tropical variety T (I) of a prime ideal I generated by the polynomials f1, . . . , fr and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that I has a short tropical basis of cardinality at most r+codim I +1 at the price of increased degrees, and we provide a… (More)