Quasi-linear complexity describes an algorithm’s computational resource usage that grows slightly faster than linearly with the size of its input. Mathematically, it is often expressed as O(N log N) or O(N log^k N), where N is the input size. This level of efficiency is considered highly desirable for processing large datasets or computations. Algorithms with quasi-linear complexity are generally practical for many real-world applications, including those in cryptography and data processing.
Context
Achieving quasi-linear complexity in cryptographic primitives and blockchain algorithms is a continuous goal for enhancing scalability and performance. News reports on advancements in zero-knowledge proofs, data compression, and consensus mechanisms often highlight efforts to reduce computational complexity to this level. Optimizing for quasi-linear complexity is essential for supporting a high volume of transactions and users on decentralized networks.
Cauchyproofs, a new batch-updatable vector commitment, achieves quasi-linear state proof updates, fundamentally solving the computational bottleneck for stateless blockchain adoption.
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