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UnInformed Search

UnInformed Search. What to do when you don’t know anything. What to know. Be able to execute (by hand) an algorithm for a problem Know the general properties Know the advantages/disadvantages Know the pseudo-code Believe you can code it. Assumptions of State-Space Model.

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UnInformed Search

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  1. UnInformed Search What to do when you don’t know anything

  2. What to know • Be able to execute (by hand) an algorithm for a problem • Know the general properties • Know the advantages/disadvantages • Know the pseudo-code • Believe you can code it

  3. Assumptions of State-Space Model • Fixed number of operators • Finite number of operators • Known initial state • Known behavior of operators • Perfect Information • Real World  Micro World • What we can do.

  4. Concerns • State-space: tree vs graph? • Are states repeated? • Completeness: finds a solution if one exists • Time Complexity • Space Complexity: Major problem • Optimality: finds best solution • Assume Directed Acyclic graphs (DAGS) • no cycles • Later: adding knowledge

  5. General Search Algorithm • Current State = initial state • While (Current State is not the Goal) • Expand State • compute all successors/ apply all operators • Store successors in Memory • Select a next State • Set Current state to next • If current state is goal: success, else failure

  6. Derived Search Algorithms • Algorithm description incomplete • What is “store in memory” • What is “memory” • What is “select” • Different choices yield different methods.

  7. Abstract tree for evaluation • Let T be a tree where each node has b descendants. B is the branching factor. • Suppose that a goal lies at depth d. • If goal is root, depth of solution is 0. • Unlike in theory, tree usually generated dynamically.

  8. Depth First • Storage = Stack • Add = push • Select = Pop • Not complete (if infinite or cycles, otherwise complete) • Not optimal • Time: O(b^m), space O(bm) where m is max depth.

  9. Ex. DFS for Permutations of 3 • Initial State: <-> • Next State: add to front, no repeats • Stack: { <->} • Next Stack: { <1>,<2>,<3>} • Next Stack: < <1,2>, <1,3>, <2>, <3>} etc • Trick: encode states with legal operators • <->  <-,{1,2,3}> • How much memory? O(n^2)

  10. Breadth First • Memory = Queue • Store = add to end • Select = take from the front • Properties: • complete, • optimal: min of steps • Time/Space Complexity = • 1+b+b^2…+b^d = [b^(d+1) -1 ]/ (b-1) = O(b^d) • Problem: Exponential memory Size.

  11. Ex. BFS for Permutations of 3 • Init: <-> • Queue: { <->} • Next Queue { <1>, <2>, <3>} • Next Queue { <2>,<3>, <1,2>, <1,3>} • So what’s the big deal? • Space n!*n for n! search.

  12. Uniform Cost • Now assume edges have positive cost • Storage = Priority Queue: scored by path cost • or sorted list with lowest values first • Select- choose minimum cost • add – maintains order • Check: careful – only check minimum cost for goal • Complete & optimal • Time & space like Breadth.

  13. Uniform Cost Example • Root – A cost 1 • Root – B cost 3 • A -- C cost 4 • B – C cost 1 • C is goal state. • Why is Uniform cost optimal? • Expanded does not mean checked node.

  14. Watch the queue • R/0 // Path/path-cost • R-A/1, R-B/3 • R-B/3, R-A-C/5: • Note: you don’t test expanded node • You put it in the queue • R-B-C/4, R-A-C/5

  15. Depth Limited • Depth First search with limit = l • Algorithm change: states not expanded if at depth k. • Complete : no • Time: O(b^k) • Space: O(b*l) • Complete if solution <=l, but not optimal.

  16. Iterative Deepening • Set l = 0 • Repeat • Do depth limited search to depth l • l = l+1 • Until solution is found. • Complete & Optimal • Time: O(b^d) • Space: O(bd) when goal at depth d

  17. Comparison Breadth vs ID • Branching Factor 10 • Depth Breadth ID 0 1 1 1 11 12 2 111 123 3 1111 1234 4 11111 12345

  18. Bidirectional • Won’t work with most goal predicates • Needs identifiable goal states • Needs reversible operators. • Needs a good hashing functions to determine if states are the same. • Then: O(b^d/2) time if bf is b in both directions.

  19. Bidirectional Search • Simple Case: • Initial State = {Start State+ Goal State} • Operators: • forward from start, backwards from goal • Standard: Breadth in both directions • Check: newly generated states intersect fringe. (can be expensive)

  20. Repeated States • Occurs whenever reversible operators • Occurs in many problems • Improvements • Do not return to k recent states: • cheap and non-effective • Do not return to state on path: • cycle checking: Cheap and effective • Do not return to any seen state: exponential • Memory costs increase for all algorithms

  21. Algorithm Effects • Cycles: • DFS incomplete: fix cycle checking • IDS incomplete: fix cycle checking • BFS still complete, but increased cost

  22. Grid World • Start (0,0) • Goal (8,8) • Legal moves: up, down, left, right • What happens to algorithms?

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