More advanced aspects of search

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More advanced aspects of search

• Extensions of A

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Extensions of A

• Iterated deepening A
• Simplified Memory-bounded A

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Iterative-deepening A
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Memory problems with A

• A is similar to breadth-first

• Here 2 extensions of A that improve memory
  usage.

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Iterative deepening A
How to establish the f-bounds? - initially
f(S) generate all successors record the minimal
f(succ) gt f(S) Continue with minimal f(succ)
instead of f(S)
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Example
f-limited, f-bound 100
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Example
f-limited, f-bound 120
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Example
f-limited, f-bound 125
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f-limited search
1. QUEUE lt-- path only containing the root
f-bound lt-- ltsome natural numbergt f-new
lt-- ? 2. WHILE QUEUE is not empty AND goal is
not reached DO remove the first path from
the QUEUE create new paths (to all
children) reject the new paths
with loops add the new paths with f(path) ?
f-bound to front of QUEUE
f-new lt-- minimum of current f-new
and of the minimum of new f-values which
are larger than f-bound 3. IF goal
reached THEN success ELSE report f-new
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Iterative deepening A
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Properties of IDA

• Complete and optimal
• under the same conditions as for A

• Memory
• Let ? be the minimal cost of an arc
• O( b (cost(B) /?) )
• Speed
• depends very strongly on the number of
  f-contours there are !!
• In the worst case f(p) ? f(q) for every 2
  paths
• 1 2 . N O(N2)

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Why is this optimal,even without monotonicity ??
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Properties practical

• If there are only a reduced number of different
  contours

• Else, the gain of the extended f-contour is not
  sufficient to compensate recalculating the
  previous
• In such cases

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Simplified Memory-bounded A
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Simplified Memory-bounded A

• Fairly complex algorithm.

• Optimizes A to work within reduced memory.
• Key idea

(15)
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Generate children 1 by 1
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Too long path give up
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Adjust f-values
better estimate for f(S)
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SMA an example
(15)
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Example continued
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(15)
(24)
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13
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(?)
13
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(?)
(?)
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SMA properties

• Complete If available memory allows to store
  the shortest path.
• Optimal If available memory allows to store
  the best path.
• Otherwise returns the best path that fits in
  memory.
• Memory Uses whatever memory available.
• Speed If enough memory to store entire tree
  same as A