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Lecture26 - IE 495 Lecture 26 December 5 2000 Reading for...

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IE 495 Lecture 26 December 5, 2000
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Reading for This Lecture Primary See me if you want references
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Example: Vertex Coloring Upper Bound : Order nodes by degree In order, color each node according to lowest feasible color Lower Bound : Maximum clique (in augmented graph) State Space : x i = color of i th vertex (1 ... k) Branching Rule : Branch on node with least number of feasible colors Search Strategy : It depends...
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Example: Traveling Salesman Problem IP Formulation max c T x ij Σ i x ij = 2 Σ (i,j) ∈δ (S) x ij 2 x ij integer Variables correspond to the edges of the graph
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Generating Constraints Dynamically generate violated constraints. Find the minimum cut in the fractional graph . If minimum cut is < 2, then we have a violated constraint. Otherwise, there are no violated constraints.
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Generating Columns Columns correspond to edges. Keep track of constraints currently in the LP relaxation. Columns can be constructed dynamically by examining the constraints already in the LP.
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Basic Branch and Cut
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