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Questions tagged [kd-tree]

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2 votes
1 answer
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Kd-trees excluding some splitting dimensions

I have a 12-dimensional state-space and would like to use a kd-tree to partition my data, so that nearest neighbour operations can be performed quickly. Unfortunately I have the issue that three of ...
Lord Cat's user avatar
  • 143
0 votes
1 answer
70 views

Fast construction of a static KD-tree without duplicates

From what I know, the classic way of constructing a KD-tree is with alternating dimensions and finding median at each level. In my dataset, I have a lot of duplicated points, and I want to incorporate ...
Valeria's user avatar
  • 127
2 votes
1 answer
156 views

Visualizing How of KD-tree Data Structure Splits Space

I am trying to understand how KD-tree works when we insert a node and how it splits the xy plane, please. Below $[5, 4]$ splits the xy-plane into left and right parts while $[2,6]$ splits it into top ...
Avv's user avatar
  • 505
2 votes
0 answers
127 views

Adaptive kD-trees

In classical kD-trees, the splitting dimension is chosen using a simple and systematic rule: dimensions are taken in a round-robin fashion. But extra freedom is available because you could very well ...
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0 votes
0 answers
40 views

Rank of random binary string with Bernoulli distribution

For $1\ge p_1 \ge \dots \ge p_n \ge 0$, and for $i\in[n]$ draw $k$ iid binary strings with $m$ length: $$X_{i,1},\dots,X_{i,k}\stackrel{iid}{\sim} \text{Bernoulli}(p_i)^m.$$ Viewing these binary ...
Ameer Jewdaki's user avatar
2 votes
1 answer
205 views

Lower bound for querying KD tree

In the book Computational Geometry, Algorithms and Applications there is an exercise asking: In the proof of the query time of the kd-tree we found the following recurrence: $$ Q(n)= \begin{cases}O(1)...
sn3jd3r's user avatar
  • 190
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0 answers
99 views

Find a bipartition of points using blackbox

Suppose given $n$ pair of points $P=\{(p_1,q_1),\dots,(p_n,q_n)\}$ in the plane that each pair $(p_i,q_i)\in \mathbb{R}^2$ can't belong to the same group. We want to partition points into $K$ groups ...
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