An Approximate Agreement Algorithm for Wraparound Meshes

An appropriate algorithm, the neighboring exchange, for reaching an approximate agreement in a wraparound mesh is proposed. The algorithm is characterized by its isotropic nature, which is of particular usefulness when applied in any symmetric system. The behavior of this algorithm can be depicted by recurrence relations which can be used to derive the convergence rate. The convergence rate is meaningful when the algorithm is used to synchnize clocks. The rate of synchronizing clocks is derived, and it can be applied to all wraparound meshes with practical scale. With the recurrence relations, we also prove the correctness of this algorithm.