- The branching factor is the number of successors generated by a given node.
- The effective branching factor is the number of successors generated by a "typical" node for a given search problem.
N: Total number of nodes processed.
d: Depth at which the solution node was found.
b*: Effective branching factor.
N = b* + (b*)2 + ... + (b*)d
- No closed-form solution
- Solution 1: A Close Guess
- Solution 2: Binary Search
- Select an error tolerance
- Select a high and low estimate
- Average the estimates to provide a guess for
N' using the guess for
abs(N' - N) > error, modify the low or high estimate accordingly
- Otherwise, it is within the error, so return the guess for
Pros and Cons
- Strengths of each approach:
- Solution 1 is quicker to calculate
- Solution 2 has a provable error bound
- Weaknesses of each approach:
- Solution 1 has a relatively loose error bound
- Solution 2 is subject to floating-point overflow for large values of