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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 33 (1985), S. 28-42 
    ISSN: 1436-4646
    Keywords: Acyclic Subgraph Problem ; Feedback Arc Set Problem ; Facets of Polyhedra ; Polynomial Time Algorithms ; Weakly Acyclic Digraphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The acyclic subgraph problem can be formulated as follows. Given a digraph with arc weights, find a set of arcs containing no directed cycle and having maximum total weight. We investigate this problem from a polyhedral point of view and determine several classes of facets for the associated acyclic subgraph polytope. We also show that the separation problem for the facet defining dicycle inequalities can be solved in polynomial time. This implies that the acyclic subgraph problem can be solved in polynomial time for weakly acyclic digraphs. This generalizes a result of Lucchesi for planar digraphs.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 33 (1985), S. 43-60 
    ISSN: 1436-4646
    Keywords: Facets of Polyhedra ; Linear Ordering Problem ; Triangulation Problem ; Permutation Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetD n be the complete digraph onn nodes, and letP LO n denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes ofD n (i.e. these are exactly the acyclic tournaments ofD n ). We show that various classes of inequalities define facets ofP LO n , e.g. the 3-dicycle inequalities, the simplek-fence inequalities and various Möbius ladder inequalities, and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input-output matrices, i.e. the solution of permutation resp. linear ordering problems.
    Type of Medium: Electronic Resource
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