A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Bounded boxes, Hausdorff distance, and a new proof of an interesting Helly-type theorem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Linear Programming - Randomization and Abstract Frameworks
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Unique Sink Orientations of Cubes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete & Computational Geometry
Random Edge Can Be Exponential on Abstract Cubes
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Linear programming and unique sink orientations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Combinatorial structure and randomized subexponential algorithms for infinite games
Theoretical Computer Science
The Number Of Unique-Sink Orientations of the Hypercube*
Combinatorica
Unique sink orientations of grids
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Jumping doesn't help in abstract cubes
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Simple stochastic games and p-matrix generalized linear complementarity problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Hi-index | 0.00 |
Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear. complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).