Constant-time distributed dominating set approximation

Abstract

Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree ∆, our algorithm computes a dominating set of expected size O k∆ 2/k log(∆)|DS OPT | in O k 2 rounds. Each node has to send O k 2 ∆ messages of size O(log ∆). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.

Localization and identification in networks using robust identifying codes

“…There are also numerous distributed algorithms for finding a minimum (connected) dominating set based on set cover and other well know approximations such as linear programming relaxation (e.g., [33]). In a recent work Kuhn et.…”

“…al. [33] devised a distributed algorithm for finding a dominating set with a constant runtime. The distributed algorithm uses a design parameter which provides a tradeoff between the runtime and performance.…”

Modeling Sensor Networks

“…It's only after a linear waiting time of O(n) time steps that node 1 eventually can make its decision and terminate the algorithm! Researchers have proposed to study yet another kind of distributed algorithm that overcomes the performance problems of localized algorithms, always terminating after a constant number of communication rounds [2].…”

Virtual Backbone Construction in MANETs Using Adjustable Transmission Ranges

“…The major drawback of a cluster formation approach is its relatively slow convergency, which takes O(n) rounds in the worst case. In DS formation approaches [13,15,18,28], the set of clusterheads may not be a MIS. The best DS formation algorithm takes O(1) rounds, but the DS size is unbounded in the worst case.…”