Polyhedral circuits and their applications

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Cites Work

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Computing the volume, counting integral points, and exponential sums
Arrangements of planes in space
An analytical expression and an algorithm for the volume of a convex polyhedron in \(R^ n\).
Polyèdres et réseaux. (Polyhedra and lattices)
The Ehrhart polynomial of the Birkhoff polytope
Asymptotics of multivariate sequences. I: Smooth points of the singular variety
Applications of random sampling in computational geometry. II
Counting lattice points by means of the residue theorem
Solving the knapsack problem via \(\mathbb Z\)-transform
Why Johnny the developer can't work with public key certificates. An experimental study of OpenSSL usability
Effective lattice point counting in rational convex polytopes
The problem of calculating the volume of a polyhedron is enumerably hard
Integer Programming with a Fixed Number of Variables
A threshold of ln n for approximating set cover
On Counting Lattice Points in Polyhedra
Polytope Volume Computation
Computing Volumes of Polyhedra
Constructing Arrangements of Lines and Hyperplanes with Applications
Points entiers dans les polyèdres convexes
On the Complexity of Computing the Volume of a Polyhedron
Finding simplicial subdivisions of polytopes
Two Algorithms for Determining Volumes of Convex Polyhedra
On the Division of the Plane by Lines
An optimal algorithm for intersecting line segments in the plane
On Barvinok's Algorithm for Counting Lattice Points in Fixed Dimension
Las Vegas algorithms for linear and integer programming when the dimension is small
A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
Sur un probl?me de g?om?trie diophantienne lin?aire. I. Poly?dres et r?seaux.
Lower Bounds for Approximation by Nonlinear Manifolds
Partition of Space