Mixed volume techniques for embeddings of Laman graphs

DOI10.1016/j.comgeo.2009.04.004zbMath1225.05186arXiv0805.4120OpenAlexW2037009986MaRDI QIDQ1037775

Thorsten Theobald, Reinhard Steffens

Publication date: 16 November 2009

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.4120

zbMATH Keywords

mixed volumeBernstein's theoremBKK theoryminimally rigid graphslaman graphs

Mathematics Subject Classification ID

Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (15)

The m-Bézout bound and distance geometry ⋮ The Number of Realizations of a Laman Graph ⋮ New upper bounds for the number of embeddings of minimally rigid graphs ⋮ Counting realizations of Laman graphs on the sphere ⋮ Coupler curves of moving graphs and counting realizations of rigid graphs ⋮ Radically solvable graphs ⋮ Computing the number of realizations of a Laman graph ⋮ Lower Bounds on the Number of Realizations of Rigid Graphs ⋮ On the maximal number of real embeddings of minimally rigid graphs in \(\mathbb{R}^2,\mathbb{R}^3\) and \(S^2\) ⋮ Equivalent realisations of a rigid graph ⋮ Elimination for generic sparse polynomial systems ⋮ On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs ⋮ Galois theory for general systems of polynomial equations ⋮ Solving decomposable sparse systems ⋮ Euclidean distance degree and mixed volume

Uses Software

• PHCpack

Cites Work

• Bernstein's theorem in affine space
• Mixed volumes of polytopes
• How to count efficiently all affine roots of a polynomial system
• Geometric algorithms and combinatorial optimization.
• Planar minimally rigid graphs and pseudo-triangulations
• The number of embeddings of minimally rigid graphs
• Efficient incremental algorithms for the sparse resultant and the mixed volume
• Pebble game algorithms and sparse graphs
• On graphs and rigidity of plane skeletal structures
• Combinatorial genericity and minimal rigidity
• Algorithm 795
• Using Algebraic Geometry
• The BKK root count in $\mathbf {C}^n$
• A Polyhedral Method for Solving Sparse Polynomial Systems
• Algorithms - ESA 2003
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