The edge domination problem

Chang, Gerard J.; Hwang, Shu-Yuen

doi:10.7151/dmgt.1006

Cited by 19 publications

(12 citation statements)

References 2 publications

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“…However, there are also families of graphs for which the unweighted EDS problem is polynomial-time solvable [9,18]. In particular, linear time algorithms for the unweighted version are known for trees [11] and block graphs [10].…”

Section: Introductionmentioning

confidence: 99%

Linear Time Algorithms for Generalized Edge Dominating Set Problems

Berger

Parekh

2007

Algorithmica

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We prove that a generalization of the edge dominating set problem, in which each edge e needs to be covered b e times for all e ∈ E, admits a linear time 2-approximation for general unweighted graphs and that it can be solved optimally for weighted trees. We show how to solve it optimally in linear time for unweighted trees and for weighted trees in which b e ∈ {0, 1} for all e ∈ E. Moreover, we show that it solves generalizations of weighted matching, vertex cover, and edge cover in trees.

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Section: Introductionmentioning

confidence: 99%

Linear Time Algorithms for Generalized Edge Dominating Set Problems

Berger

Parekh

2007

Algorithmica

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“…It should be noted that when is an odd cycle, an inequality that is at least as strong as inequality (10) is implied by (4) and (6) written for = . Henceforth, inequality (10) is interesting only when is an even cycle. Consider the graph \ displayed in Figure 2a and the solution which we claim to be outside of ( \ ).…”

Section: Maximal Matching Polytope and New Valid Inequalitiesmentioning

confidence: 99%

“…Consider the graph \ displayed in Figure 2a and the solution which we claim to be outside of ( \ ). When we write inequality (10) for the even cycle in \ , we can see that does not satisfy the inequality (1.5 is not greater than or equal to 2!) proving that ∉ ( \ ).…”

Section: Maximal Matching Polytope and New Valid Inequalitiesmentioning

confidence: 99%

“…In particular, the MMM problem has been shown to be NP-hard in bipartite graphs with maximum degree 3 [4], planar cubic graphs [6], and -regular bipartite graphs for any ≥ 3 [7]. On the positive side, it has been shown that the MMM problem can be solved in polynomial time in some classes of graphs including trees [8], series-parallel graphs [9], and block graphs [10].…”

Section: Introductionmentioning

confidence: 99%

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Valid Inequalities for the Maximal Matching Polytope

Tural

2019

Adıyaman University Journal of Science

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“…In contrast, MMM is polynomially solvable in certain restricted graph classes. Examples include trees [24], block graphs [18], series-parallel graphs [26], bipartite permutation graphs, and co-triangulated graphs [29]. Various approximation algorithms for MMM and MWMM have been proposed in the literature (see for instance [4,9,13,14,16,23,28]).…”

Section: Introduction and Literature Surveymentioning

confidence: 99%

Decomposition algorithms for solving the minimum weight maximal matching problem

2013

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We investigate the problem of finding a maximal matching that has minimum total weight on a given edgeweighted graph. Although the minimum weight maximal matching problem is NP-hard in general, polynomial time exact or approximation algorithms on several restricted graph classes are given in the literature. In this article, we propose an exact algorithm for solving several variants of the problem on general graphs. In particular, we develop integer programming (IP) formulations for the problem and devise a decomposition algorithm, which is based on a combination of IP techniques and combinatorial matching algorithms. Our computational tests on a large suite of randomly generated graphs show that our decomposition approach significantly improves the solvability of the problem compared to the underlying IP formulation.

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The edge domination problem

Cited by 19 publications

References 2 publications

Linear Time Algorithms for Generalized Edge Dominating Set Problems

Linear Time Algorithms for Generalized Edge Dominating Set Problems

Valid Inequalities for the Maximal Matching Polytope

Decomposition algorithms for solving the minimum weight maximal matching problem

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