Extension of the single-agent lower bound to the full feasible range

Determine whether the lower bound for one deterministic agent with flags in vertex-permuted dynamic rings, currently proved for \(\delta\geq 2n\), also holds throughout the full feasible range \(\delta\geq\lceil(n-1)/2\rceil\).

Background

For the restricted vertex-permuted ring class $VP(\delta)$, the paper establishes feasibility precisely when $\delta\geq\lceil(n-1)/2\rceil$. For a single deterministic agent equipped with flags, it proves an upper bound of $\delta(n-1)$ and a matching asymptotic lower bound of order $\delta n$, but the lower-bound construction is established only under the stronger assumption $\delta\geq 2n$.

The unresolved issue is whether the same asymptotic lower bound, and consequently the tight characterization of single-agent search time, remains valid for every feasible value of $\delta$, including the interval $\lceil(n-1)/2\rceil\leq\delta<2n$.