big data

Please help me to answer, or give me some ideas, or give me some reference answers, any answer you will get a

2. (The Range Query) Given a query range centered at q with radius r and an MBR node e,

Please provide the pruning condition (i.e., the condition to prune MBR node e) for the range query.

2(a) My idea: Pruning condition: we define d(x,y) as the distance between data node x and data node y

If d(Qr,q)>r(q)+r(Qr)

Then objects in node Qr can be safely pruned

2(b). Please formally prove the pruning condition in 2(a).