Fully Dynamic MIS in Uniformly Sparse Graphs

Authors

Krzysztof Onak, IBM Research
Baruch Schieber, New Jersey Institute of Technology
Shay Solomon, Tel Aviv University
Nicole Wein, Massachusetts Institute of Technology

Document Type

Article

Publication Date

4-1-2020

Abstract

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 m^3/8-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 m^1/2.

Identifier

85084759345 (Scopus)

Publication Title

ACM Transactions on Algorithms

External Full Text Location

https://doi.org/10.1145/3378025

e-ISSN

15496333

ISSN

15496325

Issue

2

Volume

16

Recommended Citation

Onak, Krzysztof; Schieber, Baruch; Solomon, Shay; and Wein, Nicole, "Fully Dynamic MIS in Uniformly Sparse Graphs" (2020). Faculty Publications. 5382.
https://digitalcommons.njit.edu/fac_pubs/5382