Faster methods for random sampling
Communications of the ACM
Linear programming in O(n × 3d2) time
Information Processing Letters
On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
Theory of linear and integer programming
Theory of linear and integer programming
On Lova´sz' lattice reduction and the nearest lattice point problem
Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Partition trees for triangle counting and other range searching problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A randomized algorithm for fixed-dimensional linear programming
Mathematical Programming: Series A and B
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A Fast Algorithm for the Two-Variable Integer Programming Problem
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Fixed-dimensional linear programming queries made easy
Proceedings of the twelfth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Deterministic algorithms for 2-d convex programming and 3-d online linear programming
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal point placement for mesh smoothing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact arithmetic at low cost—a case study in linear programming
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Random sampling in geometric optimization: new insights and applications
Proceedings of the sixteenth annual symposium on Computational geometry
Linear programming queries revisited
Proceedings of the sixteenth annual symposium on Computational geometry
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
Proceedings of the sixteenth annual symposium on Computational geometry
Randomizing combinatorial algorithms for linear programming when the dimension is moderately high
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Explicit and implicit enforcing: randomized optimization
Computational Discrete Mathematics
On the Complexity of Semidefinite Programs
Journal of Global Optimization
Fast 2-Variable Integer Programming
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Irregularities of Distribution, Derandomization, and Complexity Theory
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
How Can Computer Science Contribute to Knowledge Discovery?
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
n Points and One Line: Analysis of Randomized Games
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
A Random Sampling Technique for Training Support Vector Machines
ALT '01 Proceedings of the 12th International Conference on Algorithmic Learning Theory
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Detection of Infeasible Paths Using Presburger Arithmetic
COMPSAC '96 Proceedings of the 20th Conference on Computer Software and Applications
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Point containment in the integer hull of a polyhedron
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximation algorithms for array partitioning problems
Journal of Algorithms
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Subgradient and sampling algorithms for l1 regression
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Post-placement voltage island generation under performance requirement
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Violator spaces: structure and algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An optimal randomized algorithm for d-variate zonoid depth
Computational Geometry: Theory and Applications
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Output-sensitive algorithms for Tukey depth and related problems
Statistics and Computing
Violator spaces: Structure and algorithms
Discrete Applied Mathematics
Improved Binary Space Partition merging
Computer-Aided Design
Computing similarity between piecewise-linear functions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Clarkson's algorithm for violator spaces
Computational Geometry: Theory and Applications
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
ESA'11 Proceedings of the 19th European conference on Algorithms
Unique sink orientations of grids
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Covering and piercing disks with two centers
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Enumerating a subset of the integer points inside a Minkowski sum
Computational Geometry: Theory and Applications
Covering and piercing disks with two centers
Computational Geometry: Theory and Applications
The 2-center problem in three dimensions
Computational Geometry: Theory and Applications
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This paper gives an algorithm for solving linear programming problems. For a problem with n constraints and d variables, the algorithm requires an expectedOd2n+lognOdd/2+O1+Od4nlogn arithmetic operations, asn→∞. The constant factors do not depend on d. Also, an algorithm is given for integer linear programming. Let 4 bound the number of bits required to specify the rational numbers defining an input constraint or the objective function vector. Let n and d be as before. Then, the algorithm requires expected O2ddn+8ddnl nnlnn +dod4 lnn operations on numbers with do14 bits, as n→∞ , where the constant factors do not depend on d or4to other convex programming problems. For example, an algorithm for finding the smallest sphere enclosing a set of n points in Edhas the same time bound.