B-heap

A B-heap is a heap-ordered data structure similar to a binary heap, but with nodes having a higher degree (number of children). It generalizes the binary heap and can offer performance advantages in specific scenarios.

The "B" in B-heap does not necessarily stand for "binary." Instead, it denotes a heap structure employing a broader branching factor. While binary heaps have a fixed branching factor of two, B-heaps allow for a variable or parameterized branching factor. This branching factor is often chosen to optimize performance based on factors such as cache size or memory access patterns.

Key characteristics of a B-heap include:

• Heap Property: The value of each node is less than or equal to the value of its children (in a min-heap) or greater than or equal to the value of its children (in a max-heap). This maintains the heap order throughout the structure.

• Structure Property: While not always strictly enforced like the completeness property in binary heaps, B-heaps usually maintain a degree of balance to ensure reasonable performance. The specific structure property can vary depending on the particular implementation of the B-heap. Common approaches involve limiting the variance in the height of subtrees.

• Variable Degree: Nodes in a B-heap can have a varying number of children, up to a defined maximum degree. The degree of a node is the number of children it has.

B-heaps can be used to implement priority queues and are suitable for applications where efficient retrieval of the minimum (or maximum) element is required. The increased branching factor, when properly tuned, can lead to improved performance compared to binary heaps, particularly when considering memory access patterns and cache utilization. However, managing the more complex structure can also introduce overhead.