The cover time of a graph is the expected number of steps a random walker needs to visit every vertex at least once. When a new edge is added to a graph, intuition suggests the cover time should decrease because the walker has more options to move around. The paper on cover time nonlocality shows that this decrease can be highly nonlocal, meaning adding an edge between two nodes far from the bottleneck of the graph can still dramatically change the cover time. The open problem is to determine, for general families of graphs, the precise maximum multiplicative reduction in cover time achievable by adding a single edge, and to characterize which graph structures and which edge insertions achieve or approach this maximum reduction.