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Recently, Tscha and Lee proposed a fixed-size window algorithm for the multicast Log2(N,0,p) network and expressed a desire to see its extension to the Log2(N,m,p) network. Later, Kabacinski and Danilewicz generalized the fixed-size window to variable size to improve the results. In this paper, we further extend the variable-size results from the Log2(N,0,p) network to Log2(N,m,p). Note that this extension is difficult since each link in the channel graph of Log2(N,0,p) has the same blocking effect, but not so in Log2(N,m,p). We also determine the optimal window size and optimal m.