big data

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3. Range Queries Over M-Tree, prove the pruning strategy for the range query below (Hint: use the triangle inequality [30 points]: If d(Op, O)-d(O, Op)Pr+(O), then d(O O> (O) +r(O) holds and node centered at O, with radius (O) can be safely pruned. Or (Or d(Op.Q) dOr.Op) Op op dOrp Note LEx-dist4-p) _ distip, o)I and u.-distg, p) + disKp, o), p s a pivot Given a data set D, and a set of query points Q-g a', a data object o can be safely pruned if there exists an object o such that UBy LB oasjsn 42 dist(a, -) 0i O k 0 distla, 3. Range Queries Over M-Tree, prove the pruning strategy for the range query below (Hint: use the triangle inequality [30 points]: If d(Op, O)-d(O, Op)Pr+(O), then d(O O> (O) +r(O) holds and node centered at O, with radius (O) can be safely pruned. Or (Or d(Op.Q) dOr.Op) Op op dOrp Note LEx-dist4-p) _ distip, o)I and u.-distg, p) + disKp, o), p s a pivot Given a data set D, and a set of query points Q-g a', a data object o can be safely pruned if there exists an object o such that UBy LB oasjsn 42 dist(a, -) 0i O k 0 distla