Abstract
The edge dominating set problem (EDS) is to compute a minimum edge set such that every edge is dominated by some edge in it. This paper considers a variant of EDS with extensions of multiple and connected dominations combined. In the b-EDS problem, each edge needs to be dominated b times. Connected EDS requires an edge dominating set to be connected while it has to form a tree in Tree Cover. Although each of EDS, b-EDS, and Connected EDS (or Tree Cover) has been well studied, each known to be approximable within 2 (or 8/3 for b-EDS in general), nothing is known when these extensions are imposed simultaneously on EDS unlike in the case of the (vertex) dominating set problem.
We consider Connected 2-EDS and 2-Tree Cover (i.e., a combination of 2-EDS and Tree Cover), and present a polynomial algorithm approximating each within 2. Moreover, it will be shown that the single tree computed is no larger than twice the optimum for (not necessarily connected) 2-EDS, thus also approximating 2-EDS equally well. It also implies that 2-EDS with clustering properties can be approximated within 2 as well.
This work is supported in part by the Kayamori Foundation of Informational Science Advancement and JSPS KAKENHI under Grant Number 26330010.
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Fujito, T., Shimoda, T. (2016). On Approximating (Connected) 2-Edge Dominating Set by a Tree. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_12
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