Edmonds, J. (1965). Maximum matching and a polyhedron with 0-1 vertices. Journal of Research at the National Bureau of Standards, 69B, 125--130.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[3, 12] concerned with socalled large teeth. They reduce to ordinary comb inequalities [24, 25] when 10 S(H, T 1 , T t ) 3t (the smallest possible value) and teeth are not permitted to intersect. If, in addition, T = 2 for all j, we obtain the 2 matching inequalities of Edmonds [19]. Our separation heuristic for the strengthened comb inequalities is as follows. For the sake of computational tractability, we replace r(S) by k(S) for any set S in our implementation. First, we iteratively shrink sets S V c such that S # 2, 3 , x # (#(S) 2, and such that ....

J. Edmonds, "Maximum matching and a polyhedron with 0-1 vertices", J. Res. Nat. Bur. Standards, vol. 69B, pp. 125--130, 1965.

....in any way. Thus, requirement (6) is still not sufficient to guarantee the feasibility of the capacity vector. The set of links that are active in a slot must form a matching (a subset of links XcL is said to be a matching if no two links in X are incident to the same node [21] Edmonds [11] showed that the convex hull of the possible matching vectors in a graph is demed by a set of linear constraints (also known as the matching polytope) According to these constraints, in any odd set of nodes U the number of links that take part in a matching should not exceed (JUl l) 2. It follows ....

....in any odd set of nodes U should not exceed ( U] 1) 2. The following lemma describes the constraints that result from this observation. We note that Hajek and Sasaki [13] have introduced a similar lemma regarding link scheduling in a certain kind of packet radio networks. Lemma 1. Edmonds [ 11 ]) The capacity vector must satisJ) 2) 5) and the following constraints: Iwl 1) 2 vU N, IWlodd, Iwl 3 (7) The proof is based on Edmonds Theorem and can be found in [28] 7 A similar observation has been recently independently made by Tassiulas and Sarkar [25] who have considered the ....

J. Edmonds, "Maximum Matching and a Polyhedron with (0,1) Vertices", J.. of Research of the NationalBureau of Standards, Vol. 69B, pp. 125-130, 1965.

....are based on local search, in which the design of an appropriate neighborhood is crucial. An ejection chain is an embedded neighborhood construction that compounds simple moves to create more complex and powerful moves. Ejection chains generalize the alternating path constructions of graph theory [2, 7] and also generalize the well known Lin and Kernighan algorithms [14, 16] which were successfully applied to graph partitioning and traveling salesman problems. Recent applications of the ejection chain approach include [15, 27, 29, 30, 31] In this paper, we propose an ejection chain approach ....

J. Edmonds, "Maximum Matching and a Polyhedron with 0, 1-Vertices," J. Research of the National Bureau of Standards, 69B (1965) 125--130.

....are based on local search, in which the design of an appropriate neighborhood is crucial. An ejection chain is an embedded neighborhood construction that compounds simple moves to create more complex and powerful moves. Ejection chains generalize the alternating path constructions of graph theory [2, 7] and also generalize the well known Lin and Kernighan algorithms [14, 16] which were successfully applied to graph partitioning and traveling salesman problems. Recent applications of the ejection chain approach include [15, 27, 29, 30, 31] In this paper, we propose an ejection chain approach ....

J. Edmonds, "Maximum Matching and a Polyhedron with 0, 1-Vertices," J. Research of the National Bureau of Standards, 69B (1965) 125--130.

....which is a contradiction. Hence, C(Ma) must be a minimum. We have now shown how SMP can be formulated to solve the speaker matching problem faced by Axent. The next section looks at solving SMP. 3. 2 Solving the Sum Matching Problem The sum matching problem is a well solved problem (see Edmonds, [6]) In fact, it can be shown that SMP can be solved by the solving the following linear program : SLP: minimize cj xj subject to A x =1 (1) x i q r (2) iAr x 0 (3) Constraint (2) holds for every subgraph of G with 2q r 1 nodes, qr =1,2,3, where Ar is the set of arcs of the ....

J. Edmonds, "Maximum Matching and a polyhedron with 0,1 vertices", Journal of Research of the National Bureau of Standards, 69B (April-June 1965) 125-130

.... c e for each edge e of G, the minimumweight perfect matching problem is to find a perfect matching M of minimum weight P (c e : e 2 M ) One of the fundamental results in combinatorial optimization is the polynomialtime blossom algorithm for computing minimum weight perfect matchings by Edmonds [22, 23]. This algorithm serves as a primary model for the development of methods for attacking combinatorial integer programming problems. Moreover, efficient implementations of the algorithm permit the solution of large instances of matching problems that arise in practical situations. A classic ....

....of solutions can be stated as: for all edges e 2 E; if x e 0; then e is tight, and for all sets S 2 O, if Y S 0 then S is full. So we can prove that a specified perfect matching is optimal by providing a dual solution such that these conditions are satisfied. The remarkable result of Edmonds [22] is that such a proof of optimality always exists indeed, it is constructed by the blossom algorithm. At each step, Edmonds algorithm has a matching and a dual solution that together satisfy the complementary slackness conditions. As proposed by Derigs and Metz [18] we can initialize these ....

J. Edmonds, "Maximum matching and a polyhedron with 0,1 - vertices", Journal of Research of the National Bureau of Standards 69B (1965) 125--130.

.... Mitchell and Borchers (1992,1993) Location: Cornu ejols et al. 1977) Cornu ejols and Thizy (1982) Cho et al. 1983a,b) Leung and Magnanti (1989) Aardal et al. 1995,1996) Aardal (1998) Aardal and Van Hoesel (1998) Lot sizing: Pochet and Wolsey (1995) Constantino (1998) Matching: Edmonds (1965), Grotschel and Holland (1985) Network and VLSI design: Pochet and Wolsey (1992) Grotschel et al. 1992,1993,1995,1997) Bienstock and Gunluk (1996) Bienstock et al. 1998) Postman problems: Grotschel and Win (1992) Scheduling: Queyranne and Schulz (1994) Subgraph polytopes: Balas and ....

J. Edmonds (1965) "Maximum matching and a polyhedron with 0,1-vertices", Journal of Research of the National Bureau of Standards (B) 69 67--72.

.... introduced by Grotschel and Padberg [8] 9] If every tooth of a comb has exactly one vertex in common with the handle, we get Chv atal combs or simple combs, which were introduced by Chv atal [3] The Chv atal comb inequalities in turn generalize the class of Edmond s 2 matching inequalities [6], consisting of those Chv atal combs which have only teeth of cardinality two. If we allow the set of handles to be empty, the class of clique tree inequalities contains also the subtour elimination constraints x(E(W ) jW j Gamma 1, 2 jW j n Gamma 2. They correspond to those clique trees ....

J. Edmonds (1965), "Maximum matching and a polyhedron with 0,1-vertices", J. Res. Nat. Bur. Standards 69B (1965) 125--130.

....I , as, e.g. when P is defined by the edge inequalities and the nonnegativity constraints of the stable set problem. Moreover, sometimes P 1=2 = P 1 = P I as, for example, when P is the solution set of the nonnegativity constraints and the degree constraints for the matching problem; see Edmonds [27], Edmonds and Johnson [28] Even in case P 1 6= P 1=2 , the family of f0; 1 2 g cuts often contains several classes of (facetinducing) valid inequalities for P I , which are of valuable use within cutting plane algorithms for optimization over P I . This gives us motivation for studying P 1=2 . ....

J. Edmonds, "Maximum Matching and a Polyhedron with 0,1-vertices", Journal of Research of the National Bureau of Standards -- B. Mathematics and Mathematical Physics 69B (1965) 125--130.

.... Reinelt (1985) Mitchell and Borchers (1992,1993) Location: Cornu ejols et al. 1977) Cornu ejols and Thizy (1982) Cho et al. 1983a,b) Leung and Magnanti (1989) Aardal (1994) Aardal et al. 1994,1995) Aardal and Van Hoesel (1995a) Lot sizing: Pochet and Wolsey (1995) Matching: Edmonds (1965), Grotschel and Holland (1985) Network and VLSI design: Pochet and Wolsey (1992) Grotschel et al. 1992b,1993,1995) Bienstock and Gunluk (1994) Bienstock et al. 1995) Postman problems: Grotschel and Win (1992) Scheduling: Queyranne and Schulz (1994) Subgraph polytopes: Balas and ....

J. Edmonds (1965) "Maximum matching and a polyhedron with 0,1-vertices", Journal of Research of the National Bureau of Standards (B) 69 67--72.

....An interesting question is if k can be bounded from above by a function of the dimension of S. Chv atal called the minimum number of closure operations required to obtain conv(S) given a linear formulation P , the rank of P . If we return to the matching problem (5) 7) it was proved by Edmonds (1965) that the convex hull of the matching polytope is determined by inequalities (5) 6) and (9) As the oddset constraints (9) can be obtained by applying one closure operation on the linear formulation, the rank of the set of inequalities (5) and (6) is one. In general however, there is no upper ....

....and Wolsey (1988) It is interesting to observe here that the bipartite matching problem is polynomially solvable as its linear description is polynomial in the dimension of the problem. For the matching problem in general undirected graphs there is a polynomial combinatorial algorithm due to Edmonds (1965), but the traveling salesman problem is known to be NP hard. The following theorem confirms that there is a natural link between the computational complexity of a class of problems and the possibility of providing concise linear descriptions of the convex hull of feasible solutions. Before stating ....

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J. Edmonds (1965) "Maximum matching and a polyhedron with 0,1-vertices", Journal of Research of the National Bureau of Standards (B) 69 67--72.

....algorithm) If B ae fB ae X : jBj 2g then an optimal outcome can be determined in O(n 3 ) time. Proof : The problem of finding COPT is equivalent to finding a maximum weight matching in G which can be found in O(n 3 ) time [8] The weighted matching problem was first solved by Edmonds [6]. Algorithms for finding maximum weight matching are not particularly transparent and are considered to be among the most complicated polynomial algorithms in combinatorial optimization. Therefore, the following result should not be suprising: Theorem 6 If B = fB ae X : jBj 3g, then finding ....

Edmonds, J., "Maximum Matching and a Polyhedron with 0,1 Vertices," J. Res. NBS 69B (1965), pp 125-130.

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Edmonds, J. (1965). Maximum matching and a polyhedron with 0-1 vertices. Journal of Research at the National Bureau of Standards, 69B, 125--130.

No context found.

J. Edmonds, "Maximum matching and a polyhedron with 0,1-vertices," J. Res. Nat. Bur. Standards 69B, pp. 125--130, 1965.

No context found.

J. Edmonds, "Maximum matching and a polyhedron with 0,1vertices, " J. Res. Nat. Bur. Standards 69B, pp. 125--130, 1965.

No context found.

J. Edmonds, "Maximum matching and a polyhedron with 0, 1-vertices," J. Research of the National Bureau of Standards, 69B (1965) 125--130.

No context found.

J. Edmonds, "Maximum Matching and a Polyhedron with (0,1) Vertices", J. of Research of the National Bureau of Standards, Vol. 69B, pp. 125--130, 1965.

No context found.

J. Edmonds, "Maximum Matching and a Polyhedron with 0,1 Vertices," Journal of Research of the National Bureau of Standards (B) 69 (1965) 125--130.

No context found.

Edmonds, J. (1965). Maximum matching and a polyhedron with 0--1 vertices. J. Res. Natl. Bur. Stand. B, 69, 125--130.

No context found.

Edmonds, J. "Maximum matching and a polyhedron with 0,1-vertices." Journal of Research of the National Bureau of Standards 69B, 125--130, 1965.

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