Lower bounds for off-line range searching

1995 ◽  
Author(s):  
Bernard Chazelle
Keyword(s):  
Lower Bounds ◽  
Range Searching

scholarly journals Lower bounds for off-line range searching

1997 ◽  
Vol 17 (1) ◽  
pp. 53-65 ◽  
Author(s):  
B. Chazelle
Keyword(s):  
Lower Bounds ◽  
Range Searching

scholarly journals Tight Lower Bounds for Halfspace Range Searching

2012 ◽  
Vol 47 (4) ◽  
pp. 711-730 ◽  
Author(s):  
Sunil Arya ◽  
David M. Mount ◽  
Jian Xia
Keyword(s):  
Lower Bounds ◽  
Range Searching

scholarly journals Marked Ancestor Problems (Preliminary Version)

1998 ◽  
Vol 5 (7) ◽  
Author(s):  
Stephen Alstrup ◽  
Thore Husfeldt ◽  
Theis Rauhe
Keyword(s):  
Lower Bounds ◽  
Rooted Tree ◽  
Unit Cost ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Range Searching ◽  
Search Trees ◽  
Dictionary Matching ◽  
Preliminary Version ◽  
Emptiness Problem

Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the well-known predecessor problem, where the tree is a path.<br /> We show tight upper and lower bounds for this problem. The lower bounds are proved in the cell probe model, the upper bounds run on a unit-cost RAM.<br /> As easy corollaries we prove (often optimal) lower bounds on a number of problems. These include planar range searching, including the existential or emptiness problem, priority search trees, static tree union-find, and several problems from dynamic computational geometry, including intersection problems, proximity problems, and ray shooting. Our upper bounds improve a number of algorithms from various fields, including dynamic dictionary matching and coloured ancestor problems.

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