Local Fault Repair of Perfect Resource Placements in Eisenstein--Jacobi Networks (opens in new tab)

Perfect resource placements in dense Eisenstein--Jacobi (EJ) networks partition the network into hexagonal radius-$t$ service cells. This paper studies local repair of such placements after resource failures. For one failed resource, we prove that one replacement cannot cover the failed hexagon and two always suffice, giving $\rho_{\mathrm{EJ}}(t)=2$ for all $t\ge1$. Among minimum-size repairs, the sharp minimum-overlap formula $\Omega_{\mathrm{...