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Subject: Re: Minimal alpha-beta tree

Author: Gareth McCaughan

Date: 11:37:34 04/01/04

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On March 31, 2004 at 23:33:00, Mike Siler wrote:

>>> If I recall correctly, Knuth and Moore showed that the minimum number
>>> of leaf nodes the standard alpha-beta algorithm will examine when
>>> searching to depth d given a fixed branching factor of w is
>>>
>>> w^Floor(d/2) + w^Ceiling(d/2) + 1
>>
>> is not the formula:
>> w^Floor(d/2) + w^Ceiling(d/2) - 1
>
> I thought it was +1, which is also what Dr. Hyatt said in a post within
> the past couple of days.

Knuth & Moore, section 6, corollary 1:

  | If every position on levels 0, 1, ..., l-1 of a game tree
  | satisfying the conditions of Theorem 1 has exactly d successors,
  | for some fixed constant d, then the alpha-beta procedure
  | examines exactly d^floor(l/2) + d^ceiling(l/2) - 1
  | positions on level 1.



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