Auxiliary Variables

The array $\ensuremath{ {\mathbf V} }$ [1 $\ldots$ N] (for $\ensuremath{ {\mathbf V} }$ isited) is used only for proof purposes.
$\ensuremath{ {\mathbf V} }$ [k] is a sequence of node numbers. It contains the nodes already ``visited'' by a request originated at node k.
As an auxiliary variable, $\ensuremath{ {\mathbf V} }$ [k] may be read or written by any node;
Initially $\ensuremath{ {\mathbf V} }$ [k] = EMPTY for all k.