M.W. Padberg, \A note on zero{one programming", Operations Research 23 (1975) 833-837. Home/Search Document Not in Database Summary Related Articles Check |
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The Symmetric Generalized Travelling Salesman Polytope - Fischetti, Jos (1995) (Correct)
....v (1 y v ) u (1 y u ) is valid and facet de ning for P (F n fug) where u is an arbitrary value if u 2 W , whereas u = minf v (1 y v ) x; y) 2 P (F n fug) and y u = 0g holds when u 62 W . Proof. The thesis follows from the well known sequential lifting theorem (Padberg [15]) as described, e.g. in Gr otschel and Padberg [7] 2 Theorem 2.2 leads to a lifting procedure to be used to derive facet inducing inequalities for the GTSP polytope from those of the TSP polytope. To this end one has to choose any lifting sequence for the nodes, say fv 1 ; v n g, and ....
M.W. Padberg, \A note on zero{one programming", Operations Research 23 (1975) 833-837.
A Note on the Generalized Steiner Tree Polytope - Salazar (1999) (2 citations) (Correct)
....is valid and facet de ning for P (F n fug) where u is an arbitrary value if u 2 V 1 , whereas u = minf X e2E e x e X v2V nfug v (1 y v ) x; y) 2 P (F n fug) and y u = 0g holds when u 62 V 1 . Proof. Follows from the well known Sequential Lifting Theorem in Padberg [14]. 2 4 Theorem 2.2 leads to a lifting procedure to be used to derive facet inducing inequalities for the GST polytope P from those of the spanning tree polytope Q(V ) To this end one has to choose any lifting sequence for the nodes in V , say fv 1 ; v jV j g, and iteratively derive a ....
M. Padberg, \A note on zero{one programming", Operations Research 23 (1975) 833-837.
Conjunctive Cuts for Integer Programs - Martin, Weismantel (1998) (Correct)
....fl x j x j min l=1; u j 1 l (fl Gamma fl l ) fl x j (fl Gamma fl x j ) fl. In case x j = 0 the statement is clearly true. Proposition 2. 2 states the validity of the feasible set inequality for P (T [ fjg) To obtain a (strong) valid inequality for P we resort to lifting, see Padberg [1975]. Consider some permutation 1 ; n GammajT j Gamma1 of the set N n (T [ fjg) For k = 1; n Gamma jT j Gamma 1 and l = 1; u k let fl(k; l) max X i2T[fjg w i x i X i2f1 ; k Gamma1 g w i x i X i2T[fjg A Deltai x i X i2f1 ; k Gamma1 g A Deltai ....
.... In case the coefficient happens to be one we get a minimal cover inequality (Wolsey [1975] Moreover, feasible set inequalities are just the extended weight inequalities for the knapsack polytope if we choose weights w i = 1 for i 2 T (Weismantel [1997] Odd hole and clique inequalities (Padberg [1973] 1975]) for the set packing polytope are further examples of lifted feasible set inequalities. For some 0=1 matrix A 2 f0; 1g M ThetaN , consider the set packing polytope P (N; M; A; 1l; 1l) convfx 2 f0; 1g N : Ax 1lg, where 1l denotes the all one vector. Let GA = V; E) denote 3 the ....
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Padberg, M. (1975). A note on zero-one programming. Operations Research, 23:833-- 837.
A Network Dimensioning Tool - Alevras, Grötschel, Wessäly (1997) (3 citations) (Correct)
....for Y we now derive two classes of valid inequalities for X. The first class, the strengthened metric inequalities, is the result of a divide and round procedure. The second class, the band inequalities, is similar to minimal cover inequalities for the knapsack problem (see, e.g. Padberg [16]) In our case, Dahl and Stoer [2] showed that these can be strengthened, because of the reservation constraints, to the so called strengthened band inequalities. A third class of inequalities for X , that is not based on a valid inequality for Y , is that 10 of diversification band inequalities. ....
M.W. Padberg. A note on zero-one programming. Operations Research, 23(4):833--837, 1975.
The Generalized Minimum Spanning Tree Polytope and Related Polytopes - Pop (Correct)
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M.W. Padberg, A note on zero-one programming, Operations Research 23: 833-837, 1975.
Implementing the Dantzig-Fulkerson-Johnson Algorithm.. - Applegate, Bixby.. (2003) (2 citations) (Correct)
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Padberg, M. W. A note on zero-one programming. Operations Research 23,833-837.
TSP Cuts Which Do Not Conform to the Template Paradigm - Applegate, Bixby.. (2001) (3 citations) (Correct)
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Padberg, M.W.: A note on zero-one programming. Operations Research 23, 833--837, 1975.
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