On matrix factorization and finite-time average-consensus

We study the finite-time average-consensus problem for arbitrary connected networks. Viewing this consensus problem as a factorization of 1/n11^T by suitable families of matrices, we prove the existence of a finite factorization and provide tight bounds on the size of the minimal factorization by exhibiting finite-time average-consensus algorithms and bounding their runtimes. We also show that basic matrix theory yields insights into the structure of finite-time consensus algorithms.