Add to ORKGFor a convex body B, the membership question is the following: given a point x, is x in B? In this dissertation, we study the computational complexity of convex bodies in terms of the membership question. Since this question can be quite difficult to answer, we also study the computational complexity of testing membership for sets approximating a convex body. We give two new approximation constructions, along with some metric analysis of these approximations.Ph.D.MathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126843/2/3276318.pd
Convex Hulls: Complexity and Applications (A Survey) Computational geometry is, in brief, the study ...
The problem of approximating convex bodies by polytopes is an important and well studied problem. Gi...
Abstract: "We discuss the problem of computing the volume of a convex body K in R[superscript n]. We...
For a convex body B, the membership question is the following: given a point x, is x in B? In this ...
We discuss how well a given convex body B in a real d-dimensional vector space V can be approximated...
The present paper is the first part of a survey of computational convexity, a new area of applied ma...
Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a s...
This paper is the second part of a broader survey of computational convexity, an area of mathematics...
Consider the following supposedly-simple problem: compute x satisfying x ∈ S, where S is a convex se...
International audienceConvex bodies play a fundamental role in geometric computation, and approximat...
Our concern lies in solving the following convex optimization problem: GP: minimizex cT x s.t. Ax = ...
International audienceApproximating convex bodies succinctly by convex polytopes is a fundamental pr...
AbstractWe investigate the computational complexity of computing the convex hull of a two-dimensiona...
Assume K ⊂ Rd is a convex body and X is a (large) finite subset of K. How many convex polytopes are ...
Abstract. We consider the problem of determining whether a given set S in R n is approximately conve...
Convex Hulls: Complexity and Applications (A Survey) Computational geometry is, in brief, the study ...
The problem of approximating convex bodies by polytopes is an important and well studied problem. Gi...
Abstract: "We discuss the problem of computing the volume of a convex body K in R[superscript n]. We...
For a convex body B, the membership question is the following: given a point x, is x in B? In this ...
We discuss how well a given convex body B in a real d-dimensional vector space V can be approximated...
The present paper is the first part of a survey of computational convexity, a new area of applied ma...
Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a s...
This paper is the second part of a broader survey of computational convexity, an area of mathematics...
Consider the following supposedly-simple problem: compute x satisfying x ∈ S, where S is a convex se...
International audienceConvex bodies play a fundamental role in geometric computation, and approximat...
Our concern lies in solving the following convex optimization problem: GP: minimizex cT x s.t. Ax = ...
International audienceApproximating convex bodies succinctly by convex polytopes is a fundamental pr...
AbstractWe investigate the computational complexity of computing the convex hull of a two-dimensiona...
Assume K ⊂ Rd is a convex body and X is a (large) finite subset of K. How many convex polytopes are ...
Abstract. We consider the problem of determining whether a given set S in R n is approximately conve...
Convex Hulls: Complexity and Applications (A Survey) Computational geometry is, in brief, the study ...
The problem of approximating convex bodies by polytopes is an important and well studied problem. Gi...
Abstract: "We discuss the problem of computing the volume of a convex body K in R[superscript n]. We...