J. Edmonds, Matroid intersection, Annals of Discrete Mathematics, No. 4, pp. 185-204, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that linear optimization over K is polynomially equivalent to separation from K. 25 G constitute the intersection of the two matroids M i ; i = 1; 2. The problem of finding a maximum weight independent set in the intersection of two matroids can be solved in polynomial time (Lawler [84] Edmonds [40,42], Frank [49] The two (poly) matroid intersection polytope has been studied by Edmonds [42] The problem of testing whether a graph contains a Hamiltonian path is NP complete. Since this problem can be reduced to the problem of finding a maximum cordinality independent set in the intersection of ....

....the intersection of the two matroids M i ; i = 1; 2. The problem of finding a maximum weight independent set in the intersection of two matroids can be solved in polynomial time (Lawler [84] Edmonds [40,42] Frank [49] The two (poly) matroid intersection polytope has been studied by Edmonds [42]. The problem of testing whether a graph contains a Hamiltonian path is NP complete. Since this problem can be reduced to the problem of finding a maximum cordinality independent set in the intersection of three matroids, it follows that the matroid intersection problem involving three or more ....

J. Edmonds, Matroid intersection, Annals of Discrete Mathematics 4, (1979) 39-49.

....augments over this family in polynomial time. The vectors that we investigate are combinatorial in the sense that they can be interpreted as paths and cycles in a network. Similar ideas have been used earlier for designing augmentation algorithms for the matroid intersection problem (see [E70] [E79], L76] CCPS98] or [FSW99] To be more precise, let us consider the combinatorial optimization problem of intersecting two 0=1 integer programs, max c T x : Ax b; Cx d; x 2 f0; 1g n ; IIP) where A 2 Z m 1 Thetan , C 2 Z m 2 Thetan , b 2 Z m 1 , d 2 Z m 2 , and c 2 Z ....

J. Edmonds, Matroid Intersection, Annals of Discrete Mathematics 4, 39-- 49, 1979

.... graph G D with weights on the edges, and a fixed root r, how does one find the minimum weight directed subgraph H D that has edge disjoint paths from a fixed root r to each vertex v Gabow [13] gives the fastest implementation of a weighted matroid intersection algorithm due to Edmonds [8] to solve this problem optimally in O(n(m n log n) log n) time. Run Gabow s algorithm on the graph G D , with an arbitrary vertex r chosen as the root. If at least one of the directed edges (u; v) or (v; u) is picked in H D , then we add (u; v) to EH . Lemma 2.1 The graph H = V; EH ) is ....

....achieving a factor of 3 was given by Frederickson and J aJ a, through solving the more general graph augmentation problem. It is possible to obtain an approximation factor of 2 1 n by using a technique similar to the one used in Subsection 2.1. Frank and Tardos [12] extended Edmonds method [8] to show that the following problem can be solved in polynomial time: Given a directed graph G D with weights on the edges, and a fixed root r. Find the cheapest directed subgraph H D that has internally vertex disjoint paths from a fixed root r to each vertex v. Using this algorithm as a ....

J. Edmonds, Matroid intersection, Annals of Discrete Mathematics, 4, pp. 185--204, (1979).

....vertices have degree at most 2, then a depth first traversal of T with short cuts will yield a tour whose length is at most twice OPT. We now claim that the problem of finding T can be viewed as that of finding the minimum weight, maximum cardinality subset in the intersection of two matroids [29, 15, 16]. The two matroids in this case are: M 1 , the matroid of all bipartite forests, and M 2 , the matroid of all bipartite subgraphs whose blue vertices have degree at most 2. For completeness we review here the definition of a matroid, following the standard text [29] APPROXIMATING CAPACITATED ....

....finding a minimum weight bipartite spanning tree where the blue vertices have degree at most two, is equivalent to the problem of finding a minimum weight common base of M 1 and M 2 . This is a special case of the matroid intersection problem, which was first solved in polynomial time by Edmonds [15, 16]. Other authors [9] have exploited the special structure of problems such as ours to improve the running times. We obtain the following theorem. Theorem 2.1. There is a polynomial time 2 approximation algorithm for the Bipartite TSP. 2.1. Extension to Finite Capacity Vehicles. We will now show ....

J. Edmonds. Matroid intersection. Annals of Discrete Mathematics, 4:39--49, 1979.

....vertices have degree at most 2, then a depth first traversal of T (with short cuts) will yield a tour whose length is at most twice OPT. We now claim that the problem of finding T can be viewed as that of finding the minimum weight, maximumcardinality subset in the intersection of two matroids [27, 12, 13]. The two matroids in this case are: M 1 , the matroid of all bipartite forests, and M 2 , the matroid of all bipartite subgraphs whose blue vertices have degree at most 2. For completeness we review here the definition of a matroid, following the standard text [27] Definition 1 A matroid M = ....

....finding a minimumweight bipartite spanning tree where the blue vertices have degree at most two, is equivalent to the problem of finding a minimum weight common base of M 1 and M 2 . This is a special case of the matroid intersection problem, which was first solved in polynomial time by Edmonds [12, 13]. Other authors [8] have exploited the special structure of problems such as ours to improve the running times. We obtain the following theorem. Theorem 1 There is a polynomial time 2 approximation algorithm for the Bipartite TSP. 2.1 Finite Capacity Robot Arms We will now show how to obtain a ....

J. Edmonds. Matroid intersection. Annals of Discrete Mathematics, 4:39--49, 1979.

....as the intersection of nitely many matroids (see Theorem 5) One of the most important results in this context was given by Edmonds [4] who proved that the optimization problem over the intersection of two matroids is solvable in polynomial time. Algorithms for this problem were given by Edmonds [5], Frank [6] and Lawler [11, 12] Unfortunately, this approach fails in the case of three or more matroids. Since the (asymmetric) traveling salesman problem can be written as the intersection of three matroids, the problem of optimizing over the intersection of three or more matroids is ....

J. Edmonds, Matroid Intersection, Annals of Discrete Mathematics 4 (1979), pp. 39-49

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J. Edmonds, Matroid intersection, Annals of Discrete Mathematics, No. 4, pp. 185-204, 1979.

No context found.

J. Edmonds [1979]: Matroid intersection. Annals of Discrete Mathematics 4, 39-49.

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J. Edmonds [1979]: Matroid intersection. Annals of Discrete Mathematics 4, 39-49.

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J. Edmonds, Matroid intersection, Annals of Discrete Mathematics, 4 (1979), pp. 185-204.

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