ArrayedRadix

ArrayedRadix is a theoretical data structure designed for efficient storage and retrieval of data based on a radix or base representation. It extends the concept of traditional radix trees or tries by organizing nodes in a multi-dimensional array. This array-based structure aims to leverage the advantages of both array indexing and the hierarchical nature of radix structures.

The core idea behind ArrayedRadix is to map parts of a data key to indices within an array. Instead of each node in a radix tree having a variable number of children, in ArrayedRadix, a node's children are typically stored in a fixed-size array. The specific index within this array is determined by a segment of the data's key. This segmentation and mapping process is defined by a radix or base value. For instance, if using a base of 10, a key might be broken into digits, and each digit would correspond to an index in the child array.

This approach can potentially offer performance benefits in certain scenarios. By using array indexing, direct access to child nodes can be achieved, which can be faster than pointer traversal in traditional tree structures. However, it also introduces trade-offs. The fixed-size nature of the child arrays can lead to wasted space if many potential branches are unused, a problem known as sparsity. The efficiency of ArrayedRadix is highly dependent on the choice of radix, the data distribution, and the implementation details. It is often considered in specialized applications where predictable data access patterns and fixed-width key segments are common.