An efficient algorithm for the Riemannian 10j symbols

TL;DR

This paper introduces a significantly more efficient algorithm for computing the Riemannian 10j symbols, reducing computational complexity from previous methods, with practical implementation available online.

Contribution

The paper presents a novel algorithm that computes the 10j symbol with lower computational complexity and space requirements than existing methods.

Findings

Reduced computational complexity to order(j^5) operations

Implemented an algorithm with order(j^6) operations and constant space

Implementation available online for practical use

Abstract

The 10j symbol is a spin network that appears in the partition function for the Barrett-Crane model of Riemannian quantum gravity. Elementary methods of calculating the 10j symbol require order(j^9) or more operations and order(j^2) or more space, where j is the average spin. We present an algorithm that computes the 10j symbol using order(j^5) operations and order(j^2) space, and a variant that uses order(j^6) operations and a constant amount of space. An implementation has been made available on the web.