TY - GEN
T1 - Deterministic dominating set construction in networks with bounded degree
AU - Friedman, Roy
AU - Kogan, Alex
N1 - Funding Information: This work is partially supported by the Israeli Science Foundation grant 1247/09 and by the Technion Hasso Plattner Center.
PY - 2011
Y1 - 2011
N2 - This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usually significantly smaller than n, the total number of nodes in the system. Such networks arise in various settings of wireless and peer-to-peer communication. A trivial approach of choosing all nodes into the dominating set yields an algorithm with the approximation ratio of Δ+1. We show that any deterministic algorithm with non-trivial approximation ratio requires Ω(log* n) rounds, meaning effectively that no o(Δ)-approximation deterministic algorithm with a running time independent of the size of the system may ever exist. On the positive side, we show two deterministic algorithms that achieve logΔ and 2logΔ-approximation in O(Δ3+log* n) and O(Δ2logΔ+log* n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.
AB - This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usually significantly smaller than n, the total number of nodes in the system. Such networks arise in various settings of wireless and peer-to-peer communication. A trivial approach of choosing all nodes into the dominating set yields an algorithm with the approximation ratio of Δ+1. We show that any deterministic algorithm with non-trivial approximation ratio requires Ω(log* n) rounds, meaning effectively that no o(Δ)-approximation deterministic algorithm with a running time independent of the size of the system may ever exist. On the positive side, we show two deterministic algorithms that achieve logΔ and 2logΔ-approximation in O(Δ3+log* n) and O(Δ2logΔ+log* n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.
UR - http://www.scopus.com/inward/record.url?scp=78751675707&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-17679-1_6
DO - https://doi.org/10.1007/978-3-642-17679-1_6
M3 - منشور من مؤتمر
SN - 364217678X
SN - 9783642176784
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 65
EP - 76
BT - Distributed Computing and Networking - 12th International Conference, ICDCN 2011, Proceedings
T2 - 12th International Conference on Distributed Computing and Networking, ICDCN 2011
Y2 - 2 January 2011 through 5 January 2011
ER -