Economical convex coverings and applications

Analysis of algorithms and problem complexity (68Q25) Integer programming (90C10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Approximation by convex sets (52A27)

Cites Work

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Tight lower bounds for halfspace range searching
A randomized sieving algorithm for approximate integer programming
Measures of symmetry for convex sets and stability
How hard is half-space range searching?
The difference body of a convex body
The effect of corners on the complexity of approximate range searching
Sampling methods for shortest vectors, closest vectors and successive minima
From the Mahler conjecture to Gauss linking integrals
Factoring polynomials with rational coefficients
Geometric algorithms and combinatorial optimization
The approximation of convex sets by polyhedra
Lattice reduction: a toolbox for the cryptoanalyst
Entropy and asymptotic geometry of non-symmetric convex bodies
Approximation of general smooth convex bodies
On the combinatorial complexity of approximating polytopes
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
Approximating CVP to within almost-polynomial factors is NP-hard
Asymptotic estimates for the largest volume ratio of a convex body
Approximate CVP\(_p\) in time \(2^{0.802n}\)
Covering convex bodies and the closest vector problem
Approximate CVP in time \(2^{0.802 n}\) -- now in any norm!
Metric entropy of some classes of sets with differentiable boundaries
Shallow packings, semialgebraic set systems, macbeath regions, and polynomial partitioning
On the Blaschke-Santaló inequality
A theorem on non-homogeneous lattices
The technique of \(M\)-regions and cap coverings: A survey
A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations
Optimal area-sensitive bounds for polytope approximation
Algorithms for the Shortest and Closest Lattice Vector Problems
Integer Programming with a Fixed Number of Variables
Thrifty Approximations of Convex Bodies by Polytopes
Fine approximation of convex bodies by polytopes
Minkowski's Convex Body Theorem and Integer Programming
Convex bodies, economic cap coverings, random polytopes
Asymptotic estimates for best and stepwise approximation of convex bodies I
The Santaló-regions of a convex body
A random polynomial-time algorithm for approximating the volume of convex bodies
Optimal Approximate Polytope Membership
The Hörmander Proof of the Bourgain–Milman Theorem
Flag approximability of convex bodies and volume growth of Hilbert geometries
Economical Delone Sets for Approximating Convex Bodies
A sieve algorithm for the shortest lattice vector problem
Covering cubes and the closest vector problem
Enumerative Lattice Algorithms in any Norm Via M-ellipsoid Coverings
The directions of the line segments and of the r ‐dimensional balls on the boundary of a convex body in Euclidean space
Optimal Bound on the Combinatorial Complexity of Approximating Polytopes

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