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We read on Wikipedia > Iterative deepening depth-first search that

The space complexity of IDDFS is O(bd), where b is the branching factor and d is the depth of shallowest goal.

Wikipedia also gives some decent pseudocode for IDDFS; I pythonified it:

def IDDFS(root, goal):
  depth = 0
  solution = None
  while not solution:
    solution = DLS(root, goal, depth)
    depth = depth + 1
  return solution

def DLS(node, goal, depth):
  print("DLS: node=%d, goal=%d, depth=%d" % (node, goal, depth))
  if depth >= 0:
    if node == goal:
      return node

    for child in expand(node):
      s = DLS(child, goal, depth-1)
      if s:
        return s

  return None

So my question is, how does the space complexity include the branching factor? Does that assume that expand(node) takes up O(b) space? What if expand uses a generator that only takes constant space? In that case, would the space complexity still be a function of the branching factor? Are there situations where it is even possible for expand to be a constant-space generator?

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1 Answer 1

up vote 4 down vote accepted

You're right. Wikipedia is wrong! Does anyone have the book referenced on Wikipedia to find out what they mean (maybe they're talking about an optimization of some sort)?

Check out http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.288 and http://intelligence.worldofcomputing.net/ai-search/depth-first-iterative-deepening.html

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It feels rather self-serving to accept an answer that says I am right and wikipedia is wrong, but oh well. ;) Thanks for the response to my santiy-check. –  Dan Burton Sep 16 '11 at 0:08
1  
Am I wrong or is iterative deepening (in chess at least) used with a transposition table (cache of positions) so branches times depth is the cache size (space used)? –  Kevin Aug 7 '12 at 3:32

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