Interaction combinators can be evaluated using a path traversing strategy. That is, instead of applying annihilation/commutation rules to active pairs, one simply walks through the graph using a 2-stack machine to keep track of the exit ports.
It is known that this strategy, used naively, can have an exponential slowdown in relation to the former strategy. But that doesn't consider the possibility of jumps. Suppose that, instead of merely walking through the graph, the cursor also keeps track of the nodes it passed through. It it comes back to the same node, it jumps directly to the node whose active port would-be to interact with that one.
Is it possible to use this strategy to evaluate interaction combinators? Can it be as efficient as the graph-reduction view?