# What is the anayslsis that a heap's optimal branching factor is 2 <= factor <=5?

I'm reading the book Advanced Algorithms and Data Structures and it makes the claim that the optimal branching factor for a heap is 2 <= D <= 5 and that it is most likely 3 or 4 depending on the data being stored.

There is no citation in that book, so I tried to find one. On Wikipedia's D-ary Heap page I find two references cited for this claim. The 2nd one citation is the book Data Structures and Algorithm Analysis in C++ which contains no citations but makes the same assertions as Advanced Algorithms.

The first wikipedia citation is a 1983 book Data Structures and Network Algorithms by Robert Tarjan that simply states:

An analysis of the constant factor involved in the timing of the heap operations suggests that the choice d = 3 or 4 dominates the choice d = 2 in all circumstances, although this requires experimental confirmation.

Is there a paper with this analysis or did anybody verify this claim experimentally?