Abstract
In this paper we consider a generalization of the edge dominating set (EDS) problem, in which each edge e needs to be covered b e times and refer to this as the b-EDS problem. We present an exact linear time primal dual algorithm for the weighted b-EDS problem on trees with b e ∈ {0,1}, and our algorithm generates an optimal dual solution as well. We also present an exact linear time algorithm for the unweighted b-EDS problem on trees. For general graphs we exhibit a relationship between this problem and the maximum weight matching problem. We exploit this relationship to show that a known linear time \(\frac{1}{2}\)-approximation algorithm for the weighted matching problem is also a 2-approximation algorithm for the unweighted b-EDS problem on general graphs.
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Berger, A., Parekh, O. (2005). Linear Time Algorithms for Generalized Edge Dominating Set Problems. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_21
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DOI: https://doi.org/10.1007/11534273_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28101-6
Online ISBN: 978-3-540-31711-1
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