A Linearithmic Time Algorithm for a Shortest Vector Problem in Compute-and-Forward Design

TL;DR

This paper introduces a new algorithm with expected O(n log n) complexity for a specific shortest vector problem in compute-and-forward design, significantly improving efficiency over existing methods.

Contribution

The paper presents the first linearithmic time algorithm for a special shortest vector problem in compute-and-forward design, outperforming previous algorithms.

Findings

Algorithm achieves expected O(n log n) complexity

Outperforms previous algorithms in efficiency

Applicable to compute-and-forward design problems

Abstract

We propose an algorithm with expected complexity of $\bigO(n\log n)$ arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm is more efficient than the best known algorithms with proved complexity.