G. N. Frederickson. Approximation algorithm for some postman problems. J. ACM, 26:538--554, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that the polyhedron corresponding to the linear relaxation of this program has half integral extreme points. In this paper, we present a similar integer linear programming formulation of the mixed Chinese postman problem. We then show that a related flow problem first formulated by Frederickson [4] can be used to provide a more concise and intuitive proof of the half integrality property than was previously known. 2 Definitions An undirected graph G = V; E) is a set of vertices V along with a multiset of edges E that connect the vertices in V . An edge hu; vi is an unordered pair of ....

....00 : 1 c e 00 : c e We do the same for each oriented edge copy in E. Now solving a capacitated transshipment problem on G 0 is equivalent to solving (8) and (10) 15) We know that such a problem has an integer optimum. Hence (8) and (10) 15) does also. 2 It is interesting to note that in [4], Frederickson used the solution of this flow problem as part of a heuristic solution procedure for solving the mixed Chinese postman problem. See [4] for more details. Now for the primary results of this paper. Proposition 3 Every integral solution of (8) and (10) 15) can be mapped into a ....

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Frederickson, G.N. Approximation Algorithms for Some Postman Problems. J. of the Assoc. of Comptng. Machinery 26 (1979), 538-554.

....it completes the set of edges into an undirected cycle cover. The second part of Theorem 2.4 holds for this case as well. Algorithm ShortArcs greatly simplifies when applied to RPP and, turns to be a straightforward generalization of Christofides algorithm for TSP. As indicated by Frederickson [6], it produces 4 a 3 2 approximation algorithm for the problem (see the survey [5] for more details and [11] for a generalization) We denote by Algorithm RuralPostman the algorithm which executes these two algorithms and returns the shorter solution. Remark 2.5 In some of our algorithms for ....

G. N. Frederickson, "Approximation algorithms for some postman problems," J. Assoc. Comput. Mach. 26 (1979), pages 538-554.

....ratio of 2. Several other papers have appeared in the literature on the WPP, its LP formulation, and related solution techniques [8, 13] The reader is referred to one of several comprehensive surveys [1, 2, 5, 6, 17] for more references to postman problems. Edmonds and Johnson [4] Frederickson [7], Christo des et al. [3] and Ragavachari and Veerasamy [14] have presented approximation algorithms for the Mixed Postman Problem (MPP) Frederickson showed that the algorithm of [4] nds a tour which costs at most twice the cost of an optimal tour (i.e. approximation ratio of 2) He also ....

....0 = 1 never occurs in the ow output (Step 5(c) hence there are no undirected edges in the solution. Therefore, this LP solution is an optimal solution for even degree input graphs. 4. 1 Overview of the WPP algorithm Our algorithm is similar in its overall structure to the algorithms for MPP [7, 14]. But it di ers signi cantly in some of the crucial steps. Our algorithm nds two solutions for the windy postman problem and selects the solution of minimum cost between the two. Both solutions are based on the half integral optimal solution x to the LP formulation of the problem. The rst ....

G. N. Frederickson. Approximation algorithms for some postman problems. J. Assoc. Comput. Mach., 26:538-554, 1979.

....to design good approximation algorithms for this problem. Previous work: Numerous articles have appeared in the literature over the past three decades about the mixed postman problem. Edmonds and Johnson [3] and Christofides [2] presented the first approximation algorithms. Frederickson [7] showed that the algorithm of [3] finds a tour whose length is at most 2 times the length of an optimal tour (i.e. approximation ratio of 2) He also presented a mixed strategy algorithm, which used the solutions output by two different heuristics, and then selected the shorter of the two tours. ....

....to the output of Inoutdegree on an even degree graph; restores even degree to all nodes without increasing the cost. Edmonds and Johnson [3] indicated that Inoutdegree can be applied to an even degree graph in such a way that the resulting graph has even degree and hence Eulerian. Frederickson [7] showed a simple linear time algorithm to perform the task. The basis of this algorithm is that a suitably defined subgraph of undirected edges and duplicated edges arcs forms a collection of Eulerian graphs. ffl Largecycles: similar to Evendegree except that only edges are allowed to be ....

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G. N. Frederickson. Approximation algorithms for some postman problems. J. Assoc. Comput. Mach., 26:538--554, 1979.

.... the optimal tour of a Euclidean Traveling Salesman (and in fact any symmetric TSP obeying the triangle inequality) can be approximated by a tour of length at most one and a half times the optimal tour [Ch] Such approximation algorithms are available also for some generalizations of the TSP (see [BCCM, BGSW, Fre, FHK, Fri1, Fri2, JP, RS]) In this paper we construct algorithms with a bounded error ratio for some important cases of the Traveling Salesman with Neighborhoods Problem. If all the neighborhoods are translates of each other, we can think of our problem as a sweeper problem: Given a broom of some shape, and points in ....

Frederickson, G.N. (1979), "Approximation Algorithms for some Postman Problems", J. ACM 26, 538-554.

....it completes the set of edges into an undirected cycle cover. The second part of Theorem 2.4 holds for this case as well. Algorithm ShortArcs greatly simplifies when applied to RPP and, turns to be a straightforward generalization of Christofides algorithm for TSP. As indicated by Frederickson [6], it produces a 3 2 approximation algorithm for the problem (see the survey by Eiselt et al. 5] for more details and a paper by Jansen [11] for a generalization) We denote by Algorithm RuralPostman the algorithm which executes these two algorithms and returns the shorter solution. Remark 2.5 ....

G. N. Frederickson, "Approximation algorithms for some postman problems," J. Assoc. Comput. Mach. 26 (1979), pages 538-554.

....it completes the set of edges into an undirected cycle cover. The second part of Theorem 2.4 holds for this case as well. Algorithm ShortArcs greatly simplifies when applied to RPP and, turns to be a straightforward generalization of Christofides algorithm for TSP. As indicated by Frederickson [6], it produces a 3 2 approximation algorithm for the problem (see the survey by Eiselt et al. 5] for more details and a paper by Jansen [11] for a generalization) We denote by Algorithm RuralPostman the algorithm which executes these two algorithms and returns the shorter solution. Remark 2.5 ....

G. N. Frederickson, "Approximation algorithms for some postman problems," J. Assoc. Comput. Mach. 26 (1979), pages 538-554.

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G. N. Frederickson. Approximation algorithm for some postman problems. J. ACM, 26:538--554, 1979.

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G. N. Frederickson. Approximation algorithms for some postman problems. J. ACM, 26(3):538--554, 1979.

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