On Computational Complexity of Clifford Algebra

TL;DR

This paper explores the computational complexity of Clifford algebras, introduces a new basis for even Clifford algebra that simplifies calculations, and applies these findings to a graph theory NP-complete problem.

Contribution

It presents a novel basis for even Clifford algebra that reduces computational complexity without using matrix isomorphism, and applies this to graph problems.

Findings

New basis simplifies Clifford algebra calculations

Achieves the same complexity as traditional methods

Applied to maximum clique problem in graphs

Abstract

After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last part we apply these results to the Clifford algebra formulation of the NP-complete problem of the maximum clique of a graph introduced in a previous paper.