Lecture26 - IE 495 Lecture 26 December 5 2000 Reading for This Lecture Primary See me if you want references Example Vertex Coloring Upper Bound

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Unformatted text preview: IE 495 Lecture 26 December 5, 2000 Reading for This Lecture Primary ¡ See me if you want references 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... 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 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. Generating Columns Columns correspond to edges....
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This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

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Lecture26 - IE 495 Lecture 26 December 5 2000 Reading for This Lecture Primary See me if you want references Example Vertex Coloring Upper Bound

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