改变阵列的顺序(usort changing Array's order)

 嗯，它可以在某种程度上并行化。 它如下： 
 
 最初，所有边缘都按升序排序。 有一个main thread实际上从头开始扫描每个边缘，并决定添加当前边缘是否形成周期。 我们将算法并行化的主要目的是使这些检查并行。 
 
 这是我们使用worker threads 。 每个线程都有一定数量的边来检查，每个线程在每次迭代后检查其边是否与当前表示形成一个循环（迭代意味着主线程添加新边）。 当主线程继续添加边时，一些线程看到某些边已经与当前表示形成一个循环。 
 
 这些边缘被标记为discarded 。 当主线程到达这样的边缘时，它只是移动到下一个边缘而不对其进行任何检查。 
 
 因此，我们实际上已经将这些检查并行，这意味着算法快速运行以提高效率。 
 
 事实上，有一篇很好的论文使用了与上述相同的想法。 
 
 编辑： 
 
 如果您非常关心整体算法的运行时间，您甚至可以最初使用并行排序算法，如@ jarod42建议的那样。 

Well, it can be parallelized to some extent. It is as follows:
 
Initially all the edges are sorted in the ascending order. There is a main thread which actually scans each edge from the beginning and decides whether adding the current edge forms the cycle. Our main aim in parallelizing the algorithm is to make these checks parallel.
 
This is where we use the worker threads. Each thread is given certain number of edges to examine, where in each thread checks if its edges form a cycle with the current representation after every iteration (iteration means the main thread adding a new edge). As the main thread keeps on adding the edges, some threads see that certain edges are already forming a cycle with the current representation.
 
Such edges are marked as discarded. When the main thread reaches such edges, it simply moves on to the next one without making any check on it. 
 
Thus, we have actually made these checks parallel, which means the algorithm runs quickly increasing the efficiency.
 
In fact, there is a nice paper that uses the same idea described above.
 
EDIT:
 
If you are pretty much concerned about the running time of over-all algorithm, you can even use a parallel sorting algorithm initially as @jarod42 suggested.