Fast Computation of Generalized Dedekind Sums

TL;DR

This paper presents an algorithm that significantly improves the efficiency of computing generalized Dedekind sums, reducing the complexity from exponential to polynomial time using group theory techniques.

Contribution

The authors introduce a novel polynomial-time algorithm for computing generalized Dedekind sums based on an efficient group-theoretic rewriting process.

Findings

Reduced computational complexity from exponential to polynomial time

Demonstrated efficiency of the algorithm through theoretical analysis

Applicable to a broad class of Dedekind sums

Abstract

We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.