btrie

Btrie, short for binary trie, is a tree-based data structure designed to store keys that are sequences of bits. In a btrie, each node has at most two children, corresponding to the bit values 0 and 1. A key is represented by the path from the root to a terminal node that marks the end of the key. Keys with common prefixes share a portion of their paths, which is the main feature of trie-based structures.

Operations commonly supported by a btrie include insertion, exact search, and deletion. It also supports prefix-based queries and longest-prefix matching, where the most specific key along the traversed path is returned or identified. The time complexity for these operations is proportional to the length of the key, making tries efficient for bit-by-bit processing. The memory usage grows with the number of keys and their lengths, but prefix sharing can reduce redundancy compared with storing keys separately.

Variants and optimizations exist to address memory usage and performance. A common enhancement is path compression or node merging, leading to compact tries such as Patricia tries, which collapse single-child chains to save space while preserving fast lookups. Other approaches involve iterative or iterative-deletion strategies, and storing auxiliary data at nodes to accelerate certain queries or to support counts.

Applications for btries include IP routing tables, where longest-prefix matching is essential, firewall rule evaluation, and other scenarios requiring fast prefix or bit-string lookups. They are also used for sets of fixed-length or variable-length bitstrings and as foundational structures in text processing and networking software.