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1) I came across a picture (see below) that shows an example of R+-Tree with some data in it. How it is possible that there is a space between the nodes "A" and "B"? As i understood, any new nodes are created by splitting procedure, so they are always must share some border between them, that is a result of applying a "splitting plane". All i can think up is that the picture is a result of complex series of adding-deleting-rebuilding operations...

2) Lets suppose we have an R+-Tree composed of nodes "A" and "B" (see picture 2) and we are trying to insert a green rectangle G in this R+-Tree. The G hits "A" and "B" nodes (so must be added in both). But how "A" and "B" nodes must be expanded? (G must entirely be covered by a nodes).

picture

enter image description here

pavelkolodin
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  • You seem to be confusing k/d-trees with R-trees here. R+ trees are a mixture of both, but the main layout is borrowed from R-trees, that do *not* us the splitting plane approach – Niklas B. Mar 24 '14 at 19:09
  • Niklas B. so splitting algorithm for R+-trees can split a node by a 2 nodes that doesn't compose the original (unsplitted) node? – pavelkolodin Mar 24 '14 at 19:40
  • I think a node is always represented by some kind of bounding box around the leafs it contains. But I don't really know R-trees (the Wikipedia article is informative though) – Niklas B. Mar 24 '14 at 19:41
  • @Niklas B. a node is always has a bounding box around the leafs it contains - true, but question is much deeper than that thought ) – pavelkolodin Mar 24 '14 at 20:39
  • I was just commenting on the part "As i understood, any new nodes are created by splitting procedure, so they are always must share some border between them" which seems to be a misunderstanding. But yeah, I don't know R-trees at all, so I cannot give you a complete answer – Niklas B. Mar 24 '14 at 20:42
  • @Niklas B. but you don't explain what exactly is wrong with my statement. – pavelkolodin Mar 24 '14 at 20:45

1 Answers1

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This figure is really bad.

R-tree uses minimum bounding boxes to represent data. Therefore, the boxes must be tight, and complete; otherwise search will be inefficient or even incorrect.

Has QUIT--Anony-Mousse
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  • "This" - which one of two? This pictures is about R+-tree, not R-tree :) – pavelkolodin Mar 27 '14 at 11:08
  • Both. The R+-tree is a simple variation of the R-tree, which allows objects to be in multiple leaves. I don't know if it ever was used in practise, actually - the gains seem to be minimal, the implementation overhead large. – Has QUIT--Anony-Mousse Mar 29 '14 at 10:32
  • i have an article (please google "the r+-tree a dynamic index for multidimensional objects") says that r+-tree achieve up to 50% savings in disk access compared to an R-tree when searching files of thousands of rectangles. Disk access/memory access - no matter :) – pavelkolodin Mar 30 '14 at 23:03