Linear complexity, in the context of algorithms or protocols, describes a system where resource consumption increases directly with the size of the input or workload. For distributed ledger technologies, processing more transactions or data demands a proportional increase in computational effort. This scaling behavior is generally regarded as efficient for many operations.
Context
When assessing the performance of new cryptographic protocols or consensus algorithms, linear complexity is a preferred attribute, indicating predictable resource allocation. Discussions in crypto news often compare systems with linear scaling to those with higher-order complexities, especially when addressing transaction throughput limitations. Achieving linear scalability is a goal for many projects seeking to manage a growing user base and transaction volume without excessive costs.
Researchers introduce a new Asynchronous Verifiable Secret Sharing protocol, achieving linear communication complexity with optimal Byzantine resilience, foundational for scalable, trust-minimized computation.
A novel Validated Strong BFT model permits leader-based coordination in asynchronous networks, dramatically reducing message complexity for scalable SMR.
New authenticated Byzantine agreement protocol achieves optimal O(ft+t) communication complexity by adapting to the actual number of failures, significantly boosting SMR efficiency.
This optimistic consensus design fundamentally challenges the quadratic communication lower bound, enabling optimal scalability for distributed state machine replication.
Rondo introduces batched asynchronous verifiable secret sharing with partial output, cutting message complexity to linear for scalable, reconfigurable randomness beacons.
Achieving optimal linear prover time for zero-knowledge proofs fundamentally solves the scalability bottleneck for verifiable computation and ZK-Rollups.
A novel DAG-based consensus protocol leverages Trusted Execution Environments to significantly improve scalability, reduce communication overhead, and ensure censorship resistance.
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