Reduce turn restrictions or virtual-channel resources while preserving minimal adaptivity

Determine whether an alternative routing construction for periodic degree-six triangular-lattice tori can preserve comparable minimal adaptivity while using fewer forbidden turns or fewer virtual-channel resources than the two-forbidden-turn, two-VC Hamiltonian-dateline construction.

Background

The proposed torus routing relation forbids two directed turns and uses two virtual channels with Hamiltonian datelines to obtain an acyclic complete resource channel-dependency graph. The paper proves that assigning one virtual channel to every hop of this particular physical relation produces a cycle for n ≥ 3, but it does not establish that two virtual channels are necessary for all minimal routing relations or all flow-control mechanisms.

The authors therefore leave unresolved whether a different design can retain comparable minimal adaptivity with fewer turn restrictions or fewer virtual-channel resources. This is a concrete design and lower-bound question rather than a limitation already settled by the paper’s results.