Cost of Iterative Deepening
In general, (b - 1) / b of the nodes of a search tree are on the bottom row. If the branching factor is b = 2, half the nodes are on the bottom; with a higher branching factor, the proportion on the bottom row is higher.
Korf calculates the work done by iterative deepening as bd * (1 - 1/b)-2, where the multiplier approaches 1 as b increases.[Korf, Richard E., ``Depth-First Iterative-Deepening: An Optimal Admissible Tree Search,'' Artificial Intelligence. vol. 27, no. 1, pp. 97-112, Sept. 1985.]
My calculation of the work multiplier for iterative deepening is (b + 1) / (b - 1), which is not far from Korf's result. The multiplier is a constant, independent of depth.
| b | multiplier |
| 2 | 3.00 |
| 3 | 2.00 |
| 4 | 1.67 |
| 5 | 1.50 |
| 10 | 1.22 |