Trading accuracy for speed in approximate consensus

Approximate consensus is an important building block for distributed systems, used overtly or implicitly in applications as diverse as formation control, sensor fusion, and synchronization. Laplacian-based consensus, the current dominant approach, is extremely accurate and resilient, but converges slowly. Comparing Laplacian-based consensus to exact consensus algorithms, relaxing the requirements for accuracy and resilience should enable a spectrum of algorithms that incrementally tradeoff accuracy and/or resilience for speed. This manuscript demonstrates that may be so by beginning to populate this spectrum with a new approach to approximate consensus, Power-Law-Driven Consensus (PLD-consensus), which accelerates consensus by sending values across long distances using a self-organizing overlay network. Both a unidirectional and bidirectional algorithm based on this approach are studied. Although both have the same asymptotic O(diameter) convergence time (vs. O(diameter) for Laplacian-based), unidirectional PLD-consensus is faster and more resilient than bidirectional PLD-consensus, but exhibits higher variance in the converged value.