Performance Analysis of the Solving Algorithm for the Kuramoto Model with Rank One Coupling

TL;DR

This paper analyzes the efficiency of a pruning algorithm for finding equilibria in the Kuramoto model with rank one coupling, demonstrating its effectiveness even in worst-case scenarios through graph-based performance modeling.

Contribution

It provides a detailed performance analysis of the pruning method used in an algorithm for the Kuramoto model, highlighting its robustness in worst-case conditions.

Findings

Pruning effectively skips cases with no solutions.

Graph-based analysis models worst-case performance.

Algorithm outperforms previous methods in efficiency.

Abstract

This paper is a follow up to a previous work that presented an algorithm to efficiently find all of the equilibria of the Kuramoto model with nonuniform coupling described by a rank one matrix. The algorithm was shown experimentally to be more efficient than previously used methods, but its performance was not fully characterized. This paper analyzes the effectiveness of the "pruning" method used to skip cases with no solutions. The approach utilized is to construct a weighted graph where every path through the graph corresponds to the algorithm's performance on an input. The maximum weight path then corresponds to the worst case performance of the algorithm. This paper shows that even in the worst case, the pruning method employed is very effective at skipping cases with no solutions.