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 closed-form solution
• Solution 1: A Close Guess
  • N(1/d)
• 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 floating-point overflow for large values of d