On-line algorithms for the dominating set problem

doi:10.1016/S0020-0190(96)00191-3

Information Processing Letters

Volume 61, Issue 1, 14 January 1997, Pages 11-14

https://doi.org/10.1016/S0020-0190(96)00191-3 Get rights and content

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Cited by (17)

On the advice complexity of the online dominating set problem
2021, Theoretical Computer Science
Citation Excerpt :
Otherwise, the graph consists only of isolated vertices, and G is optimal. Moreover, it is known that there is no better deterministic online algorithm for DominatingSet on general graphs [27]. Considering optimal algorithms, we get the following almost matching bounds.
A dominating set S of a graph is a set of vertices such that each vertex is in S or has a neighbor in S. The goal of the dominating set problem is to find such a set of minimum cardinality. In the online setting, the graph is revealed vertex by vertex, together with edges to all previously revealed vertices.
Advice complexity is a framework to measure the amount of information an online algorithm is lacking. Here, an online algorithm reads advice bits from an infinite binary tape prepared beforehand by an all-knowing oracle. The advice complexity is the total number of advice bits read during the computation. Besides giving some insight into what makes an online problem hard, advice complexity can also be used as a means for proving lower bounds on the competitive ratio achievable by randomized online algorithms.
We analyze the advice complexity of the online dominating set problem. For general graphs, we show tight upper and lower bounds for optimality. Then, we use a result for c-competitiveness to prove that no randomized online algorithm can be better than $n^{1 - ε}$ -competitive, for any $ε > 0$ . Finally, we analyze the advice complexity of various graph classes for optimality.
Online Dominating Set and Coloring
2024, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Online Dominating Set and Coloring for Geometric Intersection Graphs
2023, arXiv
Online landmark replacement for out-of-sample dimensionality reduction methods
2023, arXiv
Stable Approximation Algorithms for Dominating Set and Independent Set
2023, Leibniz International Proceedings in Informatics, LIPIcs
Online dominating set and independent set
2021, arXiv

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^☆: This research was supported in part by the National Science Council, Taiwan, R.O.C., under grant NSC 86-2213-E-009-024.

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On-line algorithms for the dominating set problem☆

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Discrete Appl. Math.

Inform. Process. Lett.

J. Algorithms