An error-correcting code is said to be locally testable if it has an efficient spot-checking procedure that can distinguish codewords from strings that are far from every codeword...
The (undirected) Node Connectivity Augmentation (NCA) problem is: given a graph J = (V, EJ ) and connectivity requirements {r(u, v) : u, v ∈ V }, find a minimum size set I of n...