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Let G be a hypercube on n bits. For vertices u , v in { 0 , 1 } ^ n , bit - fixing
Let G be a hypercube on n bits. For vertices u v in n bitfixing scheme decides a path from u v by scanning the bit strings corresponding to u and v from the most significant bit to the least significant bit and flips the individual bits in order. That is correct the mismatched bits in order.
Now consider the following variant of the bitfixing scheme. Each packet pv for v in n randomly orders the position of bits in the string of its source v and corrects the mismatched bits in order of this new random string Show that there is a permutation for which with high probability this algorithm requires n steps to complete the routing.
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