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b_tree

ABSTRACT

Data structure used to manage large amounts of data efficiently

Maintain sorted data and allow for logarithmic time complexity for search / insert / delete operations

Structure / Properties​

  • Each node in a B-Tree can contain
    • number of keys (m)
    • up to m-1 children
  • For balance
    • All nodes maintain a minimum number of keys
    • All leaf nodes are at the same level
NOTE

The height of a B-Tree is logarithmic relative to the number of keys, ensuring efficient access

Operations​

  1. Start at root
  2. Recursively traverses down tree
  3. At each node
    • Check if key present OR
    • Determine which child node to explore based on comparisons with the keys in the node

Insert​

  1. Find appropriate leaf node
  2. If node full (max number of keys)
    1. split into two nodes
    2. Promote a key to parent node
  3. Continue up the key if necessary

Delete​

  1. Locate key
  2. if internal node
    1. Replace with in-order predecessor / successor

Ensure that nodes maintain minimum key requirement

References