K-d tree

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Export map as:

Research this topic

Explore the main themes, entities and connections around K-d tree. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Operations on k-d trees

Median Subtree Balanced Balanced trees Select

20 related topics

Open source implementations

ALGLIB C#C++CGAL SciPy

7 related topics

Description

Binary tree Hyperplane Half-spaces Normal

4 related topics

Variations

Rectangles Hyperrectangles Orthogonal range search Interval tree

4 related topics

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Delete: O ( log ⁡ n ) {\displaystyle O(\log n)}
Insert: O ( log ⁡ n ) {\displaystyle O(\log n)}
Invented: 1975
Invented by: Jon Louis Bentley
Operation: Average
Search: O ( log ⁡ n ) {\displaystyle O(\log n)}

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Computer science
Tree Tree data structure
Space-partitioning Space partitioning
Data structure
Points Point (geometry)
Space Euclidean space
Dimensions Dimension
Range searches Range search
Nearest neighbor searches Nearest neighbor search
Point clouds Point cloud
Binary space partitioning

Description

Binary tree
Hyperplane
Half-spaces Half-space (geometry)
Normal Surface normal

Operations on k-d trees

Median
Subtree Tree (data structure)
Balanced Balanced tree
Balanced trees
Select Selection algorithm
Algorithm
Heapsort
Mergesort
Invariant Invariant (computer science)
Subtree
Plane Plane (mathematics)
Ray tracing Ray tracing (graphics)
Computer graphics
Search tree Binary search tree
Tree-rotation Tree rotation
Bkd-tree K-D-B-tree
Adaptive k-d trees Adaptive k-d tree
Nearest neighbour search
Hypersphere
Best-bin-first search

Degradation in performance with high-dimensional data

Curse of dimensionality

Degradation in performance when the query point is far from points in the k-d tree

Tree search algorithm

Complexity

Median of medians

Variations

Rectangles Rectangle
Hyperrectangles Hyperrectangle
Orthogonal range search Orthogonal range searching
Interval tree

Open source implementations

ALGLIB
C# C Sharp (programming language)
C++
CGAL
SciPy
Python Python (programming language)
Scikit-learn

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Nodes58

Edges57

Triples88

Avg. degree1.97

Density0.034483

Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

K-d tree

Top relations

related to Points only in leaves · 8

K-d tree → Approximate, It, Maneewongvatana, Mount, Otherwise, The, This, Using

related to Volumetric objects · 8

K-d tree → For, If, In, Instead, Otherwise, See, The, Thus

related to Complexity · 7

K-d tree → Building, Finding, Heapsort, Inserting, Mergesort, Querying, Removing

related to Adding elements · 6

K-d tree → Adding, First, If, Once, One, The

related to Balancing · 6

K-d tree → Balancing, Bkd-tree, K-D-B-tree, Many, Several, They

related to Construction · 6

K-d tree → As, For, Note, Points, Since, The

related to Removing elements · 6

K-d tree → Another, First, For, Replace, Then, To

related to Degradation in performance when the query point is far from points in the k-d tree · 5

K-d tree → Additionally, Every, In, This, To

related to Description · 5

K-d tree → Every, In, Points, So, The

related to Nearest neighbour search · 4

K-d tree → NN, Searching, The, This

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

tree points k-d point search algorithm node nearest splitting plane median balanced trees current displaystyle log space range case distance

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
K-d tree	Delete	O ( log ⁡ n ) {\displaystyle O(\log n)}	1.00	infobox
K-d tree	Insert	O ( log ⁡ n ) {\displaystyle O(\log n)}	1.00	infobox
K-d tree	Invented	1975	1.00	infobox
K-d tree	Invented by	Jon Louis Bentley	1.00	infobox
K-d tree	Operation	Average	1.00	infobox
K-d tree	Search	O ( log ⁡ n ) {\displaystyle O(\log n)}	1.00	infobox
K-d tree	Space	O ( n ) {\displaystyle O(n)}	1.00	infobox
K-d tree	Time complexity in big O notation	Time complexity in big O notationOperation Average Worst caseSearch O ( log ⁡ n ) {\displaystyle O(\log n)} O ( n ) {\displaystyle O(n)} Insert O ( log ⁡ n ) {\displaystyle O(\l…	1.00	infobox
K-d tree	Type	Multidimensional BST	1.00	infobox
K-d tree	is a	binary tree in which every node is a k-dimensional point	0.90	text
heapsort or mergesort to sort all n points	instance of	sort	0.80	text
a popular practice is to sort a fixed number of randomly selected points	instance of	sort	0.80	text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

Connections between topic areas Semantic bridges

Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

Min side: 3