2026-07-26T02:16:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18852 2024-03-06T11:02:44Z ddc:004 open_access

Stable Approximation Algorithms for Dominating Set and Independent Set de Berg, Mark Sadhukhan, Arpan Spieksma, Frits Dynamic algorithms approximation algorithms stability dominating set independent set 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mark de Berg and Arpan Sadhukhan and Frits Spieksma 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.27 urn:nbn:de:0030-drops-188527 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.27 eng https://creativecommons.org/licenses/by/4.0/legalcode