A Self-Stabilizing Approximation Algorithm for the Distributed Minimum k-Domination

Self-stabilization is a theoretical framework of nonmasking fault-tolerant distributed algorithms. In this paper, we investigate a self-stabilizing distributed approximation for the minimum k-dominating set (KDS) problem in general networks. The minimum KDS problem is a generalization of the well-known dominating set problem in graph theory. For a graph G = (V, E), a set Dk ⊆ V is a KDS of G if and only if each vertex not in Dk is adjacent to at least k vertices in Dk. The approximation ratio of our algorithm is Δ/k(1 + (k-1/Δ+1)), where Δ is the maximum degree of G, in the networks of which the minimum degree is more than or equal to k.

[1]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[2]  Wayne Goddard,et al.  A Synchronous Self-stabilizing Minimal Domination Protocol in an Arbitrary Network Graph , 2003, IWDC.

[3]  Felix C. Gärtner,et al.  Fundamentals of fault-tolerant distributed computing in asynchronous environments , 1999, CSUR.

[4]  R. Rajaraman,et al.  An efficient distributed algorithm for constructing small dominating sets , 2002 .

[5]  Sukumar Ghosh,et al.  Stabilizing Phase-Clocks , 1995, Inf. Process. Lett..

[6]  Roger Wattenhofer,et al.  Constant Time Distributed Dominating Set Approximation , 2022 .

[7]  Ted Herman.  Phase Clocks for Transient Fault Repair , 2000, IEEE Trans. Parallel Distributed Syst..

[8]  Shlomi Dolev,et al.  Self Stabilization , 2004, J. Aerosp. Comput. Inf. Commun..

[9]  M. Jacobson,et al.  n-Domination in graphs , 1985 .

[10]  Pradip K. Srimani,et al.  Self-stabilizing Algorithms for Minimal Dominating Sets and Maximal Independent Sets , 2003 .

[11]  Valmir Carneiro Barbosa,et al.  A distributed algorithm to find k-dominating sets , 2004, Discret. Appl. Math..

[12]  Jaikumar Radhakrishnan,et al.  Greed is good: approximating independent sets in sparse and bounded-degree graphs , 1993, STOC '94.

[13]  Shay Kutten,et al.  Fast Distributed Construction of Small k-Dominating Sets and Applications , 1998, J. Algorithms.

[14]  Peter J. Slater,et al.  Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[15]  Sayaka Kamei,et al.  A self-stabilizing algorithm for the distributed minimal k-redundant dominating set problem in tree networks , 2003, Proceedings of the Fourth International Conference on Parallel and Distributed Computing, Applications and Technologies.

[16]  Wayne Goddard,et al.  A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system graph , 2003, Proceedings International Parallel and Distributed Processing Symposium.