2025/02/13 by Daniel Ye, Ye, Daniel
Computer Science · #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Energy Efficient Wireless Sensor Networks #FOS: Computer and information sciences #Mobile Ad Hoc Networks #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2502.09440
openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 O(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 \frac nΔ+1 in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. In fact, the best we currently know is a straightforward algorithm that finds an Ω(\frac nΔ2) size independent set. We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an O(\frac nΔ2) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem.