The clade vertebrata: spines and routing in ad hoc networks

Sivakumar, R.; Das, B.; Bharghavan, V.

doi:10.1109/iscc.1998.702601

Cited by 55 publications

(16 citation statements)

References 12 publications

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“…For general graphs, the best distributed deterministic O(log Δ)-approximation algorithms have linear running time [7,23,29]. In fact, these algorithms perform no better than a trivial approach where each node collects a global view of the network by exchanging messages with its neighbors and then calculates locally a dominating set approximation by running, e.g., the centralized algorithm of Guha and Khuller [13].…”

Section: Related Workmentioning

confidence: 99%

“…Kuhn et al [19] showed that any distributed approximation algorithm for the dominating set problem with a polylogarithmic approximation ratio requires at least Ω( log n/ log log n) communication rounds. Along with that, the existing distributed deterministic algorithms incur a linear (in number of nodes) running time [7,23,29]. This worst-case upper bound remains valid even when graphs of interest are restricted to the bounded degree case, like the ones described above.…”

Section: Introductionmentioning

confidence: 96%

“…The main application of dominating sets in such networks is to provide a virtual infrastructure, or overlay, in order to achieve scalability and efficiency. Such overlays are mainly used to improve routing schemes, where only nodes in the set are responsible for routing messages in the network (e.g., [29,30]). Other applications of dominating sets include efficient power management [11,30] and clustering [3,14].…”

Section: Introductionmentioning

confidence: 99%

“…This worst-case upper bound remains valid even when graphs of interest are restricted to the bounded degree case, like the ones described above. The deterministic approximation algorithms [7,23,29] are based on the centralized algorithm of Guha and Khuller [13], which in turn is based on a greedy heuristic for the related set-cover problem [5]. Following the heuristic, these algorithms start with an empty dominating set and proceed as following.…”

Section: Introductionmentioning

confidence: 99%

“…The decision whether to join the dominating set in the above iterative process is taken based on the lexicographic order of the pair span, ID [7,23,29]. The use of IDs to break ties leads to long dependency chains, where a node cannot join the set because of another node having higher ID.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic Dominating Set Construction in Networks with Bounded Degree

Friedman

Kogan

2011

Distributed Computing and Networking

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Abstract. 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 log Δ and 2 log Δ-approximation in O(Δ 3 + log * n) and O(Δ 2 log Δ + log * n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.

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