Intro to-iterative-deepening
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Iterative Deepening Search (IDS) combines the optimality of breadth-first search with the low memory usage of depth-first search. IDS performs a depth-limited depth-first search at each level, starting from depth 0 and incrementally increasing the depth limit. This allows it to find optimal solutions while only requiring O(bd) memory like DFS. IDA* extends this idea to A* search by imposing a limit on the estimated total path cost f and iteratively relaxing that limit, reducing memory usage while maintaining completeness and optimality.
Intro to-iterative-deepening
- 1. Iterative Deepening G51IAI – Introduction to AI Andrew Parkes http://www.cs.nott.ac.uk/~ajp/
- 2. Motivations • BFS & A* – good for optimality – bad on memory, O(bd ) • DFS – solutions not guaranteed optimal: dives and misses good nodes – good for memory O(bd) • “Iterative Deepening” refers to a method that tries to combine the best of the above
- 3. Depth-Limited Search • Simply put an upper limit on the depth (cost) of paths allowed • Motivation: – e.g. inherent limit on range of a vehicle • tell me all the places I can reach on 10 litres of petrol – prevents search diving into deep solutions – might already have a solution of known depth (cost), but are looking for a shallower (cheaper) one
- 4. Depth-Limited Search • Impose an upper limit on the depth (cost) of paths allowed – Only add nodes to the queue if their depth does not exceed the bound • DepthLimitedDFS ( k ) : DFS but only consider nodes with depth d ≤ k
- 5. Trees: Depth-Limited • Depth limit of 2 would mean that children of E are ignored JB C D E F G A H I d=0 d=1 d=2 d=3 d=4
- 6. Iterative Deepening Search • Follow the BFS pattern of “search all nodes of depth d before depth d+1” • But do the search at depth d using Depth-Limited-DFS • Schematically: • IDS: k=0; while ( not success && k < depth of tree ) { Depth-Limited-DFS ( k ); k++ }
- 7. Properties of IDS • Memory Usage – Same as DFS O(bd) • Time Usage: – Worse than BFS because nodes at each level will be expanded again at each later level – BUT often is not much worse because almost all the effort is at the last level anyway, because trees are “leaf –heavy” – Typically might be at most a factor two worse
- 8. Memory Usage of A* • We store the tree in order to – to return the route – avoid repeated states • Takes a lot of memory • But scanning a tree is better with DFS
- 9. IDA* • Combine A* and iterative deepening • f is the estimate of total path cost for start to goal • IDA*: – Impose a limit on f – Use DFS to search within the f limit – Iteratively relax the limit • Greatly reduces memory usage • Can repeat far too much work, and so be slow
- 10. Summary • Algorithm IDS: – IDS : BFS plus DFS for tree search • Algorithm IDA*: – the basis of “state of the art” “complete & optimal” algorithms
- 11. Summary • BFS & A*: good for optimality, but not memory • DFS: good for memory O(bd), but not optimality • “Iterative Deepening” refers to – IDS “Iterative Deeepening Search” • mix of DFS and BFS on trees – a broad approach used for general search, with general aim to combine optimality with low memory usage of DFS • Self-Study: carefully work through “ids.ppt” • Expectations: – know about the motivations and ideas and the search pattern – do not need details of how to code IDA*
- 12. Questions?