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Seacrh property of the B⁺-tree: search keys in internal and leaf nodes

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Slideshow:

2 more very important properties of the B⁺-tree

2 more very important properties of the B⁺-tree
 
2 more very important properties of the B⁺-tree
 
Example of a B⁺-tree

Maximum 3 keys and 4 pointers in a node: ≥ 2 (= 4/2) pointers in each internal node; ≥ 2 (= 3/2) keys in each leaf node;
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• Search property of the search key values in an internal node of a B⁺-tree node
  • Property that that allow us to perform a search efficiently in a B⁺-tree:

    All keys in a (internal or leaf) node are sorted (in increasing order) Search keys in a node partitions the search key values into disjoin sub-trees: Explanation: All search keys in the left-most (= first) subtree is smaller than (<) the value k1 All search keys in the 2nd subtree have values:   k1 ≤ key value < k2 All search keys in the 3rd subtree have values:   k2 ≤ key value < k3 And so on....

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  • Example:

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• Locating the records: search keys and block pointers in a leaf node
  • Leaf nodes of a B⁺-tree contains pointers to data records (blocks) that contains the specified search key value:

    Note that

    A block pointer = a database address of a block

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• Example of a B⁺-tree
  • Example B⁺-tree (with n = 3 , #pointers = 4):

    Structure requirement:

    Internal node: 2   ≤   # pointers   ≤   4        Leaf node: 2   ≤   # keys   ≤   3