Question regarding CRUSH algorithm

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Hi, I have a question regarding CRUSH algorithm - please let me know how this works. CRUSH paper talks about how given an object we select OSD via two mapping - first one is obj to PG and then PG to OSD. 

This PG to OSD mapping is something i dont understand. It uses pg#, cluster map, and placement rules. How is it guaranteed to return correct OSD for future reads after the cluster map/placement rules has changed due to nodes coming and out?

Thanks
Girish
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