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Tropical algebraic geometry is the geometry of the tropical semi-ring (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)

Number of pages: 210 pages Thank you for reading algorithms and data structures in vlsi design obdd foundations and applications. As you may know, people have look numerous times for their favorite books like this algorithms and data structures in vlsi design obdd foundations and applications, but end up in harmful downloads. Rather than enjoying a good… (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)

- Thorsten Theobald
- J. Symb. Comput.
- 2006

We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is non-empty, whether it is a tropical variety, and whether it is connected, as well as counting the number of connected components. We characterize the borderline between tractable and hard computations by… (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.

- 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)

- I. G. MacDonald, János Pach, Thorsten Theobald
- Discrete & Computational Geometry
- 2001

- Christoph Meinel, Thorsten Theobald
- ITA
- 1997

Ordered binary decision diagrams are an important data structure for the representation 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)

- Michael Joswig, Thorsten Theobald
- Universitext
- 2013

- 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)