论文标题
具有等级耦合的库拉莫托模型的求解算法的性能分析
Performance Analysis of the Solving Algorithm for the Kuramoto Model with Rank One Coupling
论文作者
论文摘要
本文是先前作品的后续作品，该作品提出了一种算法，以有效地找到库拉莫托模型的所有平衡，并具有由等级一级矩阵描述的非均匀耦合。该算法在实验上显示为比以前使用的方法更有效，但其性能尚未完全表征。本文分析了用于跳过没有解决方案的案例的“修剪”方法的有效性。所使用的方法是构造一个加权图，其中的每个路径通过图对应于输入上的算法的性能。然后，最大重量路径对应于算法的最坏情况。本文表明，即使在最坏的情况下，使用的修剪方法在没有解决方案的情况下跳过案件也非常有效。
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.
