Polylogarithmic Runtime

Definition ∞ Polylogarithmic runtime describes an algorithm’s efficiency where its execution time grows proportionally to a polynomial of the logarithm of the input size. This indicates a highly efficient algorithm, as logarithmic growth is very slow, meaning the algorithm performs well even with extremely large inputs. It signifies excellent scalability for computational tasks. It means very efficient processing.
Context ∞ In the development of scalable blockchain solutions and zero-knowledge proofs, achieving polylogarithmic runtime for verification algorithms is a significant goal. This efficiency is critical for processing large numbers of transactions or complex computations off-chain, then verifying them quickly on-chain. Such advancements are essential for improving the throughput and reducing the costs of decentralized networks. This is key for blockchain scalability.