This paper introduces the Cartesian Merkle Tree, a deterministic data structure that combines the properties of a Binary Search Tree, a Heap, and a Merkle tree. The Cartesian Merkle Tree supports insertions, updates, and removals of elements in O(logn) time, requires n space, and enables membership and non-membership proofs via Merkle-based authentication paths. This structure is particularly suitable for zero-knowledge applications, blockchain systems, and other protocols that require efficient and verifiable data structures.
@article{arxiv.2504.10944,
title = {Cartesian Merkle Tree},
author = {Artem Chystiakov and Oleh Komendant and Kyrylo Riabov},
journal= {arXiv preprint arXiv:2504.10944},
year = {2025}
}