A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries

2010 ◽  
Vol 57 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Timothy M. Chan
Keyword(s):  
Data Structure ◽  
Nearest Neighbor ◽  
Convex Hulls ◽  
Dynamic Data ◽  
Dynamic Data Structure ◽  
Nearest Neighbor Queries

SKIP QUADTREES: DYNAMIC DATA STRUCTURES FOR MULTIDIMENSIONAL POINT SETS

2008 ◽  
Vol 18 (01n02) ◽  
pp. 131-160 ◽  
Author(s):  
DAVID EPPSTEIN ◽  
MICHAEL T. GOODRICH ◽  
JONATHAN Z. SUN
Keyword(s):  
Data Structure ◽  
Hierarchical Structure ◽  
Data Structures ◽  
Nearest Neighbor ◽  
Point Location ◽  
Dynamic Data ◽  
Higher Dimensional ◽  
Point Data ◽  
Logarithmic Height ◽  
Nearest Neighbor Queries

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R2) or the skip octree (for point data in Rd, with constant d > 2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined “box”-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location, approximate range, and approximate nearest neighbor queries.

scholarly journals THREE PROBLEMS ABOUT DYNAMIC CONVEX HULLS

2012 ◽  
Vol 22 (04) ◽  
pp. 341-364 ◽  
Author(s):  
TIMOTHY M. CHAN
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Query Time ◽  
Convex Hulls ◽  
Lower Envelope ◽  
Dynamic Data ◽  
Line Segments ◽  
3 Dimensional ◽  
Small Constant ◽  
Dynamic Data Structure

We present three results related to dynamic convex hulls: • A fully dynamic data structure for maintaining a set of n points in the plane so that we can find the edges of the convex hull intersecting a query line, with expected query and amortized update time O( log 1+εn) for an arbitrarily small constant ε > 0. This improves the previous bound of O( log 3/2n). • A fully dynamic data structure for maintaining a set of n points in the plane to support halfplane range reporting queries in O( log n+k) time with O( polylog n) expected amortized update time. A similar result holds for 3-dimensional orthogonal range reporting. For 3-dimensional halfspace range reporting, the query time increases to O( log 2n/ log log n + k). • A semi-online dynamic data structure for maintaining a set of n line segments in the plane, so that we can decide whether a query line segment lies completely above the lower envelope, with query time O( log n) and amortized update time O(nε). As a corollary, we can solve the following problem in O(n1+ε) time: given a triangulated terrain in 3-d of size n, identify all faces that are partially visible from a fixed viewpoint.

scholarly journals An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries

2012 ◽  
Vol 41 (1) ◽  
pp. 104-127 ◽  
Author(s):  
Pankaj K. Agarwal ◽  
Lars Arge ◽  
Haim Kaplan ◽  
Eyal Molad ◽  
Robert E. Tarjan ◽  
...  
Keyword(s):  
Data Structure ◽  
Dynamic Data ◽  
Optimal Dynamic ◽  
Dynamic Data Structure

scholarly journals A dynamic data structure for flexible molecular maintenance and informatics

2010 ◽  
Vol 27 (1) ◽  
pp. 55-62 ◽  
Author(s):  
C. Bajaj ◽  
R. A. Chowdhury ◽  
M. Rasheed
Keyword(s):  
Data Structure ◽  
Dynamic Data ◽  
Dynamic Data Structure
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