Omer Berkman, Baruch Schieber, et al.
Journal of Algorithms
We consider the problem of maintaining a maximal independent set in a dynamic graph subject to edge insertions and deletions. Recently, Assadi et al. (at STOC'18) showed that a maximal independent set can be maintained in sublinear (in the dynamically changing number of edges) amortized update time. In this article, we significantly improve the update time for uniformly sparse graphs. Specifically, for graphs with arboricity α, the amortized update time of our algorithm is O(α2 ⋅ log2 n), where n is the number of vertices. For low arboricity graphs, which include, for example, minor-free graphs and some classes of "real-world" graphs, our update time is polylogarithmic. Our update time improves the result of Assadi et al. for all graphs with arboricity bounded by m3/8-ϵ, for any constant ϵ > 0. This covers much of the range of possible values for arboricity, as the arboricity of a general graph cannot exceed m1/2.
Omer Berkman, Baruch Schieber, et al.
Journal of Algorithms
Lior Ben Yamin, Jing Li, et al.
APPROX/RANDOM 2020
Artur Czumaj, Slobodan Mitrović, et al.
STOC 2018
Baruch Schieber, Daniel Geist, et al.
Discrete Applied Mathematics