Computational Oriented Matroids
Computational Oriented Matroids
Zchaff2004: an efficient SAT solver
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Finding Lean Induced Cycles in Binary Hypercubes
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
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Oriented matroids are a combinatorial abstraction of finite sets of points in ℝn. They have been used to study various problems in discrete and computational geometry (for more material on oriented matroids, see [1,2]). A number of methods to generate oriented matroids have been proposed (for instance in [4,8-10]) as these methods can be used as a building block for the algorithmic treatment of some hard problems: Algorithms to generate oriented matroids have for instance been used to decide whether certain 4-polytopes exist [6,10,14]. For these questions it is important to have effective algorithms for the generation of oriented matroids. We propose to use satisfiability solvers to generate oriented matroids. We have adapted this approach to generate oriented matroids that satisfy certain geometric constraints. Even though one can use the generated oriented matroids as a first step to find realizations (see for instance [2,6]), we will only focus on non-realizability results.