We know that the decision version of Bin-packing problem is NP-complete: Given an integer B, an integer k, and a list of integers X = (x1, x2, . . . , xn) where xi ∈ [0, B], is there any partition of X into k sublists, such that each sublist sums to at most B?
But what about the special case where the given numbers x_i's are as follows: x_1 = 1, x_2 = 2, ... , x_n = n.
Then is this case also NP-complete?
In general is there any reference that I can find all or many versions of Bin-packing problem, and the facts known about them?