Combinatorial Linear Programming: Geometry Can Help
نویسنده
چکیده
We consider a class A of generalized linear programs on the d-cube (due to Matoušek) and prove that Kalai’s subexponential simplex algorithm Random-Facet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible for general instances in A. Thus, we identify a “geometric” property of linear programming that goes beyond all abstract notions previously employed in generalized linear programming frameworks, and that can be exploited by the simplex method in a nontrivial setting.
منابع مشابه
Combinatorial optimization in geometry
In this paper we extend and unify the results of [20] and [19]. As a consequence, the results of [20] are generalized from the framework of ideal polyhedra in H to that of singular Euclidean structures on surfaces, possibly with an infinite number of singularities (by contrast, the results of [20] can be viewed as applying to the case of non-singular structures on the disk, with a finite number...
متن کاملA Combinatorial Algorithm for Fuzzy Parameter Estimation with Application to Uncertain Measurements
This paper presents a new method for regression model prediction in an uncertain environment. In practical engineering problems, in order to develop regression or ANN model for making predictions, the average of set of repeated observed values are introduced to the model as an input variable. Therefore, the estimated response of the process is also the average of a set of output values where th...
متن کاملHelly-Type Theorems and Generalized Linear Programming
Recent combinatorial algorithms for linear programming can also be applied to certain non-linear problems. We call these Generalized Linear Programming, or GLP, problems. We connect this class to a collection of results from combinatorial geometry called Helly-type theorems. We show that there is a Helly-type theorem about the constraint set of every GLP problem. Given a family H of sets with a...
متن کاملAPPLICATION OF LINEAR PROGRAMMING TECHNIQUES IN PRODUCTION PLANNING
Optimum utilization of limited resources in the production floor demands that the production manager makes decisions on the best allocation of limited resources. This study applied linear programming techniques to production planning problem in a feed mill producing company. Linear Programming model was formulated based on data obtained from the company operations’ diary. Data was processed wit...
متن کاملFrom combinatorial optimization to real algebraic geometry and back
In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which r...
متن کامل