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Multidimensional Data Structures
Multidimensional Searching Problems
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0(log n 0(n log amortized applications assume atomic segments balanced tree BB[a]-trees BCH(S binary search boundary chain compute constructed contains convex hull convex polygons coordinate data structure dd-trees decomposable searching problems defined discussion dist(x,y doubly linked list dynamic elements exercise follows frame F hence in-interval insertions and deletions intersection problem interval trees leaf left endpoint Lemma linear lower bound NL(v node list number of edges orthogonal range queries pair paradigm partial match retrieval path decomposition planar graph planar subdivision plane sweep pointer polygon trees polygonal chain Pos(e prio(v priority field priority search tree query interval range trees rebalancing rectangles recursive Reg(v root rotations search structure segment tree sequence simple polygon solution solve space 0(n space requirement split split fields static data structure stored subtree suffices sweep line tion triangulation update upper convex hull VD(S vertex Voronoi diagram VR(x weighted x-coordinate xrange xrange(v y-structure