Lect4 - Announcement Homework 1 was posted to the web site...

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Announcement Homework 1 was posted to the web site yesterday Due one week from today Hand-in instruction on web site www.cs.illinois.edu/class/cs440 Requires some consolidation thought Don’t Wait 1
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Admissibility of A* (cont) 2) n nodes h(n) h*(n) Informally: be optimistic (or don’t be pessimistic) Why? Could you prove it? Important General Principle: Optimism Under Uncertainty Does not depend on problem or tree! Is “Uniform Cost” admissible? 2
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We have: Then we say “more informed” implies “guaranteed not to search more” A 1 * with heuristic fcn h 1 A 2 * with heuristic fcn h 2 A 1 * and A 2 * are admissible A 1 * is more informed than A 2 * iff for all non-goal nodes n h 1 (n) h 2 (n) 3
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But what about this? Three nodes B, C, D two A* searches A 1 and A 2 with B C D h* 10 8 11 h 1 6 7 4 h 2 5 1 3 A 1 is more informed than A 2 but won’t it search more? 4
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5 I D 4,3 C 7,1 B 6,5 G3 2 2 2 8 10 11 G2 G1 B C D h* 10 8 11 h 1 6 7 4 h 2 5 1 3 A 1 n q - (I) I (D 6 B 8 C 9 ) D (B C G3 13 ) B (C G1 12 G3) C (G2 10 G1 G3) G2 (G1 G3) A 2 n q - (I) I (C 3 D 5 B 7 ) C (D B G2 10 ) D (B G2 G3 13 ) B (G2 G1 12 G3) G2 (G1 G3)
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Other Questions? 6
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Linearity Problem / World / System Straight line / hyperplane Linear = Easy Superposition Principle: Solve(G 1 G 2 , IS) = Solve(G 1 , IS) Solve(G 2 , IS) Is the world usually linear? IS: $5, G 1 : Lunch, G 2 : Present 7
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Search as Problem Solving assume linearity? Exhaustive: No Hill Climbing: Yes Beam: Yes, partially 8
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Example Suppose we want to build a house Branching factor? ~50 (conservative) Depth? ~1000 (small house) Number of leaves in tree? 50 1000 10 1300 9
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A fast computer - assume a TeraHz machine 1,000,000,000,000 or 10 12 nodes/sec Seconds in a year? 30,000,000 or 3x10 7 sec/year Age of the Universe? 14,000,000,000 or 1.4x10 10 years We can expand 4.2x10 29 < 10 30 nodes How informed must h be? What fraction of nodes can we expand? (assuming faster-than-possible computer, start at t=0, etc…) 10
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