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- W2080656989 abstract "Given a matroid M on E and a nonnegative real vector x =( x j : j ∈ E ), a fundamental problem is to determine whether x is in the convex hull P of (incidence vectors of) independent sets of M . An algorithm is described for solving this problem for which the amount of computation is bounded by a polynomial in | E |, independently of x , allowing as steps tests of independence in M and additions, subtractions, and comparisons of numbers. In case x ∈ P , the algorithm finds an explicit representation for x which has additional nice properties; in case x ∉ P it finds a most-violated inequality of the system defining P . The same technique is applied to the problem of finding a maximum component-sum vector in the intersection of two matroid polyhedra and a box." @default.
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- W2080656989 date "1984-04-01" @default.
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- W2080656989 title "Testing membership in matroid polyhedra" @default.
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- W2080656989 doi "https://doi.org/10.1016/0095-8956(84)90023-6" @default.
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