A geometric method of sector decomposition

TL;DR

This paper introduces a deterministic geometric sector decomposition method for IR factorization, utilizing convex and combinatorial geometry algorithms to improve efficiency and avoid infinite loops.

Contribution

A novel geometric approach to sector decomposition that guarantees termination and reduces the number of sectors compared to existing methods.

Findings

Fewer sectors generated than previous methods

Algorithm guarantees termination without infinite loops

Test implementation shows improved efficiency

Abstract

We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method provides a deterministic algorithm and never falls into an infinite loop. The number of resulting sectors depends on the algorithm of triangulation. Our test implementation shows smaller number of sectors comparing with other existing methods with iterations.