eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-09-04
27:1
27:19
10.4230/LIPIcs.APPROX/RANDOM.2023.27
article
Stable Approximation Algorithms for Dominating Set and Independent Set
de Berg, Mark
1
Sadhukhan, Arpan
1
https://orcid.org/0000-0003-4048-7143
Spieksma, Frits
1
Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
We study Dominating Set and Independent Set for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is k-stable when it makes at most k changes to its output independent set or dominating set upon the arrival of each vertex. We study trade-offs between the stability parameter k of the algorithm and the approximation ratio it achieves. We obtain the following results.
- We show that there is a constant ε^* > 0 such that any dynamic (1+ε^*)-approximation algorithm for Dominating Set has stability parameter Ω(n), even for bipartite graphs of maximum degree 4.
- We present algorithms with very small stability parameters for Dominating Set in the setting where the arrival degree of each vertex is upper bounded by d. In particular, we give a 1-stable (d+1)²-approximation, and a 3-stable (9d/2)-approximation algorithm.
- We show that there is a constant ε^* > 0 such that any dynamic (1+ε^*)-approximation algorithm for Independent Set has stability parameter Ω(n), even for bipartite graphs of maximum degree 3.
- Finally, we present a 2-stable O(d)-approximation algorithm for Independent Set, in the setting where the average degree of the graph is upper bounded by some constant d at all times.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol275-approx-random2023/LIPIcs.APPROX-RANDOM.2023.27/LIPIcs.APPROX-RANDOM.2023.27.pdf
Dynamic algorithms
approximation algorithms
stability
dominating set
independent set