conference paper
A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks
Christine
Markarian
author 37612
Friedhelm
Meyer auf der Heide
author 15523
Michael
Schubert
author
63
department
SFB 901
project
SFB 901 - Subprojekt A1
project
SFB 901 - Project Area A
project
Dominating set based virtual backbones are used for rou-ting in wireless ad-hoc networks. Such backbones receive and transmit messages from/to every node in the network. Existing distributed algorithms only consider undirected graphs, which model symmetric networks with uniform transmission ranges. We are particularly interested in the well-established disk graphs, which model asymmetric networks with non-uniform transmission ranges. The corresponding graph theoretic problem seeks a strongly connected dominating-absorbent set of minimum cardinality in a digraph. A subset of nodes in a digraph is a strongly connected dominating-absorbent set if the subgraph induced by these nodes is strongly connected and each node in the graph is either in the set or has both an in-neighbor and an out-neighbor in it. We introduce the first distributed algorithm for this problem in disk graphs. The algorithm gives an O(k^4) -approximation ratio and has a runtime bound of O(Diam) where Diam is the diameter of the graph and k denotes the transmission ratio r_{max}/r_{min} with r_{max} and r_{min} being the maximum and minimum transmission range, respectively. Moreover, we apply our algorithm on the subgraph of disk graphs consisting of only bidirectional edges. Our algorithm gives an O(ln k) -approximation and a runtime bound of O(k^8 log^∗ n) , which, for bounded k , is an optimal approximation for the problem, following Lenzen and Wattenhofer’s Ω(log^∗ n) runtime lower bound for distributed constant approximation in disk graphs.
https://ris.uni-paderborn.de/download/563/1278/563-978-3-642-45346-5_16.pdf
application/pdf
2013
Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)10.1007/978-3-642-45346-5_16
217-227
C. Markarian, F. Meyer auf der Heide, M. Schubert, in: Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS), 2013, pp. 217–227.
Markarian, C., Meyer auf der Heide, F., & Schubert, M. (2013). A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks. In <i>Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)</i> (pp. 217–227). <a href="https://doi.org/10.1007/978-3-642-45346-5_16">https://doi.org/10.1007/978-3-642-45346-5_16</a>
Markarian, Christine, Friedhelm Meyer auf der Heide, and Michael Schubert. “A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks.” In <i>Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)</i>, 217–27. LNCS, 2013. <a href="https://doi.org/10.1007/978-3-642-45346-5_16">https://doi.org/10.1007/978-3-642-45346-5_16</a>.
C. Markarian, F. Meyer auf der Heide, and M. Schubert, “A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks,” in <i>Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)</i>, 2013, pp. 217–227.
Markarian C, Meyer auf der Heide F, Schubert M. A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks. In: <i>Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)</i>. LNCS. ; 2013:217-227. doi:<a href="https://doi.org/10.1007/978-3-642-45346-5_16">10.1007/978-3-642-45346-5_16</a>
Markarian, Christine, et al. “A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks.” <i>Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)</i>, 2013, pp. 217–27, doi:<a href="https://doi.org/10.1007/978-3-642-45346-5_16">10.1007/978-3-642-45346-5_16</a>.
@inproceedings{Markarian_Meyer auf der Heide_Schubert_2013, series={LNCS}, title={A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks}, DOI={<a href="https://doi.org/10.1007/978-3-642-45346-5_16">10.1007/978-3-642-45346-5_16</a>}, booktitle={Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)}, author={Markarian, Christine and Meyer auf der Heide, Friedhelm and Schubert, Michael}, year={2013}, pages={217–227}, collection={LNCS} }
5632017-10-17T12:42:42Z2019-01-03T13:17:16Z