An Efficient Algorithm for Vertex Enumeration of Two-Dimensional Projection of Polytopes

TL;DR

This paper introduces a linear-time algorithm for enumerating vertices of a 2D polytope projection using support functions, outperforming existing methods in efficiency.

Contribution

The paper presents a novel, support function-based algorithm for vertex enumeration of 2D polytope projections with improved computational complexity.

Findings

Algorithm runs in linear time relative to the number of vertices.

Empirical results show significant performance improvements over existing algorithms.

Supports efficient vertex enumeration in applications involving polytope projections.

Abstract

An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices. The complexity of our algorithm is linear in the number of vertices of the projected polytope and we show empirically that the performance is significantly better in comparison to some known efficient algorithms of projection and enumeration.