If you're just doing BFS why do you care who the parent is? Why not just choose the parent to be the predecessor? I.e if you visit 4 from 1, then 1 is the parent. Why do you need to check a list of potential parents?
When visiting vertices in parallel, there might be multiple potential parents that all attempt to visit the same vertex simultaneously. So, we need a way of picking which parent "wins".
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If you're just doing BFS why do you care who the parent is? Why not just choose the parent to be the predecessor? I.e if you visit 4 from 1, then 1 is the parent. Why do you need to check a list of potential parents?
When visiting vertices in parallel, there might be multiple potential parents that all attempt to visit the same vertex simultaneously. So, we need a way of picking which parent "wins".