3.Readtheture slides about the pruning conditions for Simple Point Method (SPM) f GNN queries, and prove the pruning condition below (Hint: you may need to read the original paper of GNN and use the triangle inequality for the proof) [30 points] mindist(N abest dist+dist(g.O Single Point Method (SPM) MQM has the problem of multiple NN queries accessing the same objects Instead, SPM computes with a centroid q of the query set Q o A centroid q(x, y) minimizing dist(q.0) =Je-x)2 +(y-y)2 a dist(q.Q. a dist(q,Q) y-y, 0 dist(q,Q 59 where y is a step size. Pruning Conditions for SPM An MBR node N can be pruned, if it holds that: best dist +dist mindist(N,q)2 1n where bestdist is the distance of the best GNN found so far best NN centroid q 4 mindist(N q-10 mindisi(N)-6 60 Minimum Bounding Method (MBM) MBM uses the minimum bounding rectangle M of Q (instead of the centroid q) to prune the search space onditions for SPM mindist(Nq)-5 M 12 2 mindist(N 'yh-3 mindist(N,M)- mindist(N2M) mindist( 29.pl best NN N2 61 Experimental Results for GNN Comparisons of three approaches o PP data sets: 24,493 populated places in North America E+4number of node accesses 1 1 CPU cost (sec) E+3 0.1 100 0.01 10 0.001 4 4 16 64256 024 64 256 1024 (a) NA vs. n (PP dataset) (b) CPU vs. n (PP dataset) D. Papadias, Q. Shen, Y. Tao, and K. Mouratidis. Group Nearest Neighbor Queries. In ICDE, 2004 3.Readtheture slides about the pruning conditions for Simple Point Method (SPM) f GNN queries, and prove the pruning condition below (Hint: you may need to read the original paper of GNN and use the triangle inequality for the proof) [30 points] mindist(N abest dist+dist(g.O Single Point Method (SPM) MQM has the problem of multiple NN queries accessing the same objects Instead, SPM computes with a centroid q of the query set Q o A centroid q(x, y) minimizing dist(q.0) =Je-x)2 +(y-y)2 a dist(q.Q. a dist(q,Q) y-y, 0 dist(q,Q 59 where y is a step size. Pruning Conditions for SPM An MBR node N can be pruned, if it holds that: best dist +dist mindist(N,q)2 1n where bestdist is the distance of the best GNN found so far best NN centroid q 4 mindist(N q-10 mindisi(N)-6 60 Minimum Bounding Method (MBM) MBM uses the minimum bounding rectangle M of Q (instead of the centroid q) to prune the search space onditions for SPM mindist(Nq)-5 M 12 2 mindist(N 'yh-3 mindist(N,M)- mindist(N2M) mindist( 29.pl best NN N2 61 Experimental Results for GNN Comparisons of three approaches o PP data sets: 24,493 populated places in North America E+4number of node accesses 1 1 CPU cost (sec) E+3 0.1 100 0.01 10 0.001 4 4 16 64256 024 64 256 1024 (a) NA vs. n (PP dataset) (b) CPU vs. n (PP dataset) D. Papadias, Q. Shen, Y. Tao, and K. Mouratidis. Group Nearest Neighbor Queries. In ICDE, 2004