Computational Geometry Column 34

Problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry are listed

Computational Geometry Column 37

Open problems from the 15th Annual ACM Symposium on Computational Geometry

Cylindrical Static and Kinetic Binary Space Partitions

P. K. Agarwal, L. Guibas, T. M. Murali, and J. S. Vitter. “Cylindrical Static and Kinetic Binary Space Partitions,” Computational Geometry, 16(2), 2000, 103–127. An extended abstract appears in Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG ’97), Nice, France, June 1997, 39–48

Cylindrical Static and Kinetic Binary Space Partitions

P. K. Agarwal, L. Guibas, T. M. Murali, and J. S. Vitter. “Cylindrical Static and Kinetic Binary Space Partitions,” Computational Geometry, 16(2), 2000, 103–127. An extended abstract appears in Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG ’97), Nice, France, June 1997, 39–48

MultivariateResidues - a Mathematica package for computing multivariate residues

We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations.Comment: 7 pages, 2 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017

Liftings and stresses for planar periodic frameworks

We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks.Comment: An extended abstract of this paper has appeared in Proc. 30th annual Symposium on Computational Geometry (SOCG'14), Kyoto, Japan, June 201

Snapping Graph Drawings to the Grid Optimally

In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space consumption as well as computation time. This process is called snapping to the grid and has been investigated thoroughly from a computational-geometry perspective. In this paper we investigate the same problem for given drawings of planar graphs under the restriction that their combinatorial embedding must be kept and edges are drawn straight-line. We show that the problem is NP-hard for several objectives and provide an integer linear programming formulation. Given a plane graph G and a positive integer w, our ILP can also be used to draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016