Branching Factor
Informal Definitions
 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.
Formal Definition

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}
Calculating b*
 No closedform solution
 Solution 1: A Close Guess
 Solution 2: Binary Search
 Requires
N
and d
 Select an error tolerance
 Select a high and low estimate
 Average the estimates to provide a guess for
b*
 Calculate
N'
using the guess for b*
and d
 If
abs(N'  N) > error
, modify the low or high estimate accordingly
 Otherwise, it is within the error, so return the guess for
b*
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 floatingpoint overflow for large values of
d