Distributed computing on anonymous hypercube networks

The authors consider the bit-complexity (i.e. the total number of bits transmitted) of computing boolean functions on an anonymous canonically labeled n-dimensional hypercube network with N=2ⁿ nodes and give a characterization of the boolean functions computable on such a network as exactly those boolean functions which are invariant under all bit-complement automorphisms of the hypercube. They provide an efficient algorithm for computing all such functions with bit complexity O(N^.log⁴ N). For the case of symmetric boolean functions they give an algorithm with bit complexity O(N^.log ² N)