9. Assume that all messages are being broadcast. Justify your answers to each of the following.

(a) Modify the causal message ordering algorithm in Figure 6.13 so that processes use only two vectors of size n, rather than the n × n array.

(b) Is it possible to implement total order using a vector of size n?

(c) Is it possible to implement total order using a vector of size O(1)?

(d) Is it possible to implement causal order using a vector of size O(1)?