Allocate tasks to servers. Server cost = sum of (task weights)^2 for assigned tasks. Find the lowest total. = min cost to assign first tasks to servers.
Transition: split at some point for the -th server. Cost of assigning to one server = . Use prefix sums. QI holds for this squared-sum cost. Apply D&C: . The squared sum cost encourages even distribution. Putting all tasks on one server gives high cost.