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L12-matching

# L12-matching - 1 Matching Polytope Matching Polytope x1 x2...

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Unformatted text preview: 1 Matching Polytope Matching Polytope x1 x2 x3 Lecture 12: Feb 22 x1 x2 x3 2 Per fect Matching But not every solution is a matching!! 3 x1 x3 x2 x1 x2 x3 Matching Polytope x1 x2 x3 4 Valid I nequalities Enough? Inequalities which are satisfied by integer solutions but kill all unwanted fractional vertex solution. everywhere everywhere 5 Valid I nequalities Enough? Odd set inequalities Yes, that’s enough. [Edmonds 1965] 6 Exponentially Many I nequalities Can take care by the ellipsoid method. Just need a separation oracle , which determines whether a solution is feasible. If not, find a violating inequality . How to construct a separation oracle for matching? 7 Rewr iting the Odd-Set Constr aints 8 Matching Polytope 9 Convex Combination A point y in R n is a convex combination of if there exist so that and 10 Ver tex Solution Fact: A solution is a vertex solution if and only if x is not a convex combination of other feasible solutions. A point y in R n is a convex combination of if y is in the convex hull of 11 Convex Combination Goal: Prove that every fractional solution can be...
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L12-matching - 1 Matching Polytope Matching Polytope x1 x2...

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