TY - JOUR
T1 - Fully Dynamic MIS in Uniformly Sparse Graphs
AU - Onak, Krzysztof
AU - Schieber, Baruch
AU - Solomon, Shay
AU - Wein, Nicole
N1 - Publisher Copyright:
© 2020 ACM.
PY - 2020/4
Y1 - 2020/4
N2 - 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.
AB - 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.
KW - Maximal independent set
KW - dynamic graph algorithms
KW - edge orientations
KW - graph arboricity
UR - http://www.scopus.com/inward/record.url?scp=85084759345&partnerID=8YFLogxK
U2 - 10.1145/3378025
DO - 10.1145/3378025
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AN - SCOPUS:85084759345
SN - 1549-6325
VL - 16
JO - ACM Transactions on Algorithms
JF - ACM Transactions on Algorithms
IS - 2
M1 - 26
ER -