Re-Rooting-Assisted Edge-Minimum Runtime Repair for Node and Link Failures in Dense Eisenstein--Jacobi Broadcast Networks (opens in new tab)

One-to-all broadcasting in dense Eisenstein--Jacobi (EJ) networks relies on diameter-level spanning trees that fragment when nodes or links fail. This paper introduces the selected triple $(r,\theta,\Kcomp_{r,\theta})$--a chosen root, a chosen EJ coordinate-reduction orientation, and the healthy component graph induced by that choice--as the fundamental unit of analysis for joint node/link fault recovery. The central result is a necessary and ...