Fully Dynamic MIS in Uniformly Sparse Graphs

Krzysztof Onak, Baruch Schieber, Shay Solomon, Nicole Wein

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Article number26
JournalACM Transactions on Algorithms
Volume16
Issue number2
DOIs
StatePublished - Apr 2020

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Keywords

  • Maximal independent set
  • dynamic graph algorithms
  • edge orientations
  • graph arboricity

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