Programming Pearl: Computing Convex Hulls with a Linear Solver

Title: Programming Pearl: Computing Convex Hulls with a Linear Solver

Abstract: This research article discusses a programming tactic that has been widely applied in the analysis of logic programs. The method enables the computation of convex hulls, which are required for polyhedral analysis, to be coded with linear constraint solving machinery that is available in many Prolog systems. The technique has been adopted in the analysis of many logic programs, and it presents an elegant solution to the problem without the need for a dual representation. The article provides an example implementation and concludes with a discussion on the method's effectiveness and implications.

Main Research Question: How can the convex hull of two polyhedra be computed efficiently using linear constraint solving machinery?

Methodology: The research proposes a method to compute the convex hull of two polyhedras, P1 and P2, represented in standard form. The method uses linear constraint solving machinery to project the problem onto a standard form and then solve it using existing algorithms. The technique has been widely adopted in the analysis of logic programs, and it presents an elegant solution to the problem without the need for a dual representation.

Results: The research demonstrates that the convex hull of P1 ∪ P2 is not necessarily closed, but the closure of the convex hull can be represented by a system of non-strict linear inequalties. The method has been successfully implemented in many logic programs, and it provides an efficient way to compute the convex hull without the need for a dual representation.

Implications: The research has significant implications for the analysis of logic programs. It provides an efficient and elegant method to compute the convex hull of polyhedras, which is essential for many polyhedral analysis techniques. The method's simplicity and effectiveness make it an attractive choice for many programmers and researchers in the field.

Conclusion: In conclusion, the research article presents a programming tactic that has been widely applied in the analysis of logic programs. The method enables the computation of convex hulls using linear constraint solving machinery, providing an efficient and elegant solution to the problem. The research has significant implications for the analysis of logic programs and presents an attractive choice for many programmers and researchers in the field.

Link to Article: https://arxiv.org/abs/0311002v1 Authors: arXiv ID: 0311002v1