Enumerating stationary multiple-points

A Problem in Enumerating Extreme Points

We describe the central problem in developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints, and discuss a conjecture for its solution.

A Practical Algorithm for Enumerating Collinear Points

This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of n points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help with other problems, such as point line cover and general position subset selection. The classic topological sweeping algorithm of Edelsbrunner and Guibas can ...

Enumerating Extreme Points in Higher Dimensions

We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present an algorithm with O(n) space and O(nm) time where m is the number of extreme points of P. We also present an algorithm to compute the depth of each point of the given set of n points in d-dimensions. This algorithm has complexity O(n 2) which signiicantly improves the O(n 3) comple...

Stationary Points and Equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path ...

Stationary Points of Transformation Groups.