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MIT16_410F10_lec07a - Solving Constraint Programs using...

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1 Solving Constraint Programs using Conflicts and Backjumping 6/30/11 1 Brian C. Williams 16.410-13 September 29 th , 2010 Slides draw upon material from: Prof. Patrick Prosser, Glasow University 2 Search Performance on N Queens Standard Search Backtracking BT with Forward Checking Dynamic Variable Ordering Iterative Repair Conflict-directed Back Jumping A handful of queens About 15 queens About 30 queens About 1,000 queens About 10,000,000 queens (except truly hard problems) 1 2 3 4 Q Q Q Q
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2 3 Back Jumping Backtracking At dead end, backup to the most recent variable . Backjumping At dead end, backup to the most recent variable that eliminated some value in the domain of the dead end variable . Example of a CSP C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Slide progression due to Prosser [4C presentation, 2003]
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3 C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Find solution using Backtracking Example of a CSP C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP
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4 C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP
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5 C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Fast forward .. Example of a CSP
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6 C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back Example of a CSP
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7 C E D B F A G H Va Vb Vc Vd Ve Vf Vg Vh 1 = red 2 = blue 3 = green Variables and Instantiation Order Checking back
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