Completely unimodal numberings of a simple polytope
Discrete Applied Mathematics
A simple way to tell a simple polytope from its graph
Journal of Combinatorial Theory Series A
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
The Generalized Order Linear Complementarity Problem
SIAM Journal on Matrix Analysis and Applications
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
Linear programming, the simplex algorithm and simple polytopes
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
The random facet simplex algorithm on combinatorial cubes
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
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
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Grid Orientations, (d,d + 2)-Polytopes, and Arrangements of Pseudolines
Discrete & Computational Geometry
The On-Line Encyclopedia of Integer Sequences
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Lower bounds for a subexponential optimization algorithm
Random Structures & Algorithms
Linear programming and unique sink orientations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Violator spaces: structure and algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Violator spaces: Structure and algorithms
Discrete Applied Mathematics
Finding a Polytope from Its Graph in Polynomial Time
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A Simple P-Matrix Linear Complementarity Problem for Discounted Games
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Optimizing a 2d function satisfying unimodality properties
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Simple stochastic games and p-matrix generalized linear complementarity problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We introduce unique sink orientations of grids as digraph models for many well-studied problems, including linear programming over products of simplices and generalized linear complementarity problems over P-matrices (PGLCP). We investigate the combinatorial structure of such orientations and develop randomized algorithms for finding the sink. We show that the orientations arising from PGLCP satisfy the combinatorial Holt-Klee condition known to hold for polytope digraphs, and we give the first expected linear-time algorithms for solving PGLCP with a fixed number of blocks.