The time complexity analysis of the IDA* algorithm has
shown that predicting the growth of the search tree essentially relies
on only two criteria: The number of nodes in the brute-force search tree
for a given depth and the equilibrium distribution of the heuristic es-
timate. Since the latter can be approximated by random sampling, we
accurately predict the number of nodes in the brute-force search tree for
large depth in closed form by analyzing the spectrum of the problem
graph or one of its factorization.
We further derive that the asymptotic brute-force branching factor is in
fact the spectral radius of the problem graph and exemplify our consid-
erations in the domain of the (n^2-1)-Puzzle.