2026-08-16T06:38:20Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23512 2025-10-02T12:57:22Z ddc:004 open_access

Deterministic Independent Sets in the Semi-Streaming Model Ye, Daniel Sublinear Algorithms Derandomization Semi-Streaming Algorithms We consider the independent set problem in the semi-streaming model. For any input graph G = (V, E) with n vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, G is presented as a stream of edges and any algorithm must use Õ(n) bits of memory to output a large independent set at the end of the stream. Prior work has designed various semi-streaming algorithms for finding independent sets. Due to the hardness of finding maximum and maximal independent sets in the semi-streaming model, the focus has primarily been on finding independent sets in terms of certain parameters, such as the maximum degree Δ. In particular, there is a simple randomized algorithm that obtains independent sets of size n/(Δ+1) in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. The best we know is a straightforward algorithm that finds an Ω̃(n/(Δ²)) size independent set. We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an Õ(n/(Δ²)) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Daniel Ye 2025 Is Part Of LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2025.135 urn:nbn:de:0030-drops-235129 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.135 eng https://creativecommons.org/licenses/by/4.0/legalcode