A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks
Markarian, Christine
Meyer auf der Heide, Friedhelm
Schubert, Michael
ddc:040
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.
2013
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https://ris.uni-paderborn.de/record/563
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>
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-642-45346-5_16
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