In this paper, we consider the problem of recognizing whether a given
network is a rectangular mesh. We present an efficient distributed alg
orithm with an O(N) message and time complexity, where N is the number
of nodes in the network. This is an improvement of a previous algorit
hm presented in Mohan (I 990) with a message complexity of O(N log N)
and time complexity of O(N1.6). The proposed algorithm is constructive
in nature and also assigns coordinates to the nodes of the network.