Sub-quadratic overhead describes a computational cost that grows slower than the square of the input size, often expressed as O(n^c) where c is less than 2. In cryptographic protocols, achieving sub-quadratic overhead is a significant efficiency improvement for operations involving large datasets. It signifies a more scalable algorithm compared to those with quadratic or higher complexity.
Context
The pursuit of sub-quadratic overhead is a major research goal in the development of scalable zero-knowledge proofs and data availability schemes for blockchains. Reducing the computational cost associated with proof generation and verification is crucial for supporting high transaction volumes. Advancements in polynomial commitments and specialized algebraic structures are actively driving the realization of protocols with this desirable efficiency characteristic.
A new k-dimensional polynomial commitment scheme drastically reduces data availability overhead, unlocking massive throughput for decentralized rollups.
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