Abstract
We study the following problem: Given a weighted graph G = (V, E, w) with \({w: E \rightarrow \mathbb{Z}^+}\) , the dominating tree (DT) problem asks us to find a minimum total edge weight tree T such that for every \({v \in V}\) , v is either in T or adjacent to a vertex in T. To the best of our knowledge, this problem has not been addressed in the literature. Solving the DT problem can yield a routing backbone for broadcast protocols since (1) each node does not have to construct their own broadcast tree, (2) utilize the virtual backbone to reduce the message overhead, and (3) the weight of backbone representing the energy consumption is minimized. We prove the hardness of this problem, including the inapproximability result and present an approximation algorithm together with an efficient heuristic. Finally, we verify the effectiveness of our proposal through simulation.
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Thai M.T., Wang F., Liu D., Zhu S., Du D.Z.: Connected dominating sets in wireless networks with different transmission ranges. IEEE Trans. Mobile Comput. 6(7), 721–730 (2007)
Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed construction on connected dominating set in wireless ad hoc networks. In: Proceedings of the Conference of the IEEE Communications Society (INFOCOM) (2002)
Guha S., Khuller S.: Approximation algorithms for connected dominating sets. Algorithmica 20, 374–387 (1998)
Park, M., Wang, C., Willson, J., Thai, M.T., Wu, W., Farago, A.: A dominating and absorbent set in wireless ad-hoc networks with different transmission range. In: Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC) (2007)
Thai M.T., Tiwari R., Du D.-Z.: On construction of virtual backbone in wireless ad hoc networks with unidirectional links. IEEE Trans. Mobile Comput. 7(8), 1–12 (2008)
Arkin E.M., Halldorssom M.M., Hassin R.: Approximating the tree and tour covers of a graph. Inform. Process. Lett. 47, 275–282 (1993)
Fujito T.: On approximability of the independent/connected edge dominating set problems. Inform. Process. Lett. 79(6), 261–266 (2001)
Fujito T.: How to trim an MST: a 2-approximation algorithm for minimum cost tree cover. ICALP 1, 431–442 (2006)
Feige U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–653 (1988)
Charikar M., Chekuri C., Cheung T., Dai Z., Goel A., Guha S., Li M.: Approximation algorithms for directed steiner tree problems. J. Algorithms 33, 73–91 (1999)
Leiserson C.E., Rivest R.L., Cormen T.H., Stein C.: Introduction to Algorithms. MIT Press, Cambridge (1976)
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Shin, I., Shen, Y. & Thai, M.T. On approximation of dominating tree in wireless sensor networks. Optim Lett 4, 393–403 (2010). https://doi.org/10.1007/s11590-010-0175-0
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DOI: https://doi.org/10.1007/s11590-010-0175-0