A new generalised consensus problem and its CRT-based solution

This technical note introduces a new generalizedconsensus problem where nodes in a network are guaranteed toreach the final consensus on a common vector whose elements areexactly the initial values arbitrarily chosen by nodes. We proposea fully decentralized algorithm able to solve the above problemand derive conditions to guarantee that consensus is reached in afinite number of steps. In particular, we prove that in a networkcomposed bynnodes, the proposed consensus problem is solvablein at most2nsteps. Moreover, we introduce a finite-field solutionbased on the Chinese Remainder Theorem (CRT) able to reducethe complexity of the proposed approach in the case of capacityconstraints, and we discuss an illustrative case study.