Quasi-optimal upper bounds for simplex range searching and new zone theorems

Algorithmica ◽  
1992 ◽  
Vol 8 (1-6) ◽  
pp. 407-429 ◽  
Author(s):  
Bernard Chazelle ◽  
Micha Sharir ◽  
Emo Welzl
Keyword(s):  
Upper 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.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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