# Fully Dynamic Maximal Independent Set with Sublinear in n Update Time

@article{Assadi2018FullyDM, title={Fully Dynamic Maximal Independent Set with Sublinear in n Update Time}, author={Sepehr Assadi and Krzysztof Onak and Baruch Schieber and Shay Solomon}, journal={ArXiv}, year={2018}, volume={abs/1806.10051} }

The first fully dynamic algorithm for maintaining a maximal independent set (MIS) with update time that is sublinear in the number of edges was presented recently by the authors of this paper [Assadi et al., STOC'18]. The algorithm is deterministic and its update time is O(m3/4), where m is the (dynamically changing) number of edges. Subsequently, Gupta and Khan and independently Du and Zhang [arXiv, April 2018] presented deterministic algorithms for dynamic MIS with update times of O(m2/3) and…

## 34 Citations

### Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time

- Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

The first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time is presented and a simpler variant of the algorithm can be used to maintain a random-order lexicographically first maximal matching in the same update-time.

### Fully Dynamic Maximal Independent Set in Expected Poly-Log Update Time

- Mathematics, Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

A dynamic randomized algorithm against oblivious adversary with expected worst-case update time of O(log^4n).

### When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear Time

- Mathematics, Computer ScienceICALP
- 2019

The results suggest that even though MIS and MM do not admit sublinear-time algorithms in general graphs, one can still solve both problems in sublinear time for a wide range of beta(G) << n.

### Fully Dynamic MIS in Uniformly Sparse Graphs

- Computer Science, MathematicsICALP
- 2018

This article significantly improves the update time for uniformly sparse graphs, and improves the result of Assadi et al. (at STOC’18) on maintaining a maximal independent set in a dynamic graph subject to edge insertions and deletions.

### Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT

- Computer Science, MathematicsFSTTCS
- 2020

This paper initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph G = (V, E), we present deterministic fully dynamic distributed and sequential algorithms to maintain a cut…

### Dynamic Near Maximum Independent Set with Time Independent of Graph Size

- Computer Science, MathematicsArXiv
- 2020

A framework based on swap operations for resolving the problem to maintain a high-quality independent set, which is an approximation of the MaxIS, over dynamic graphs is presented and two concrete update algorithms based on one- Swappable vertices and two-swappble vertex pairs are designed.

### Dynamic Approximate Maximum Independent Set on Massive Graphs

- Computer Science, Mathematics2022 IEEE 38th International Conference on Data Engineering (ICDE)
- 2022

This paper proposes a framework that maintains a $(\displaystyle \frac{\triangle}{2}+1)$ -approximate MaxIS over dynamic graphs and proves that it achieves a constant approximation ratio in many real-world networks, the first non-trivial approximability result for the dynamic MaxIS problem.

### Fast Deterministic Algorithms for Highly-Dynamic Networks

- Computer ScienceOPODIS
- 2020

An algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round, and the tasks for which an algorithm is deduced are maximal matching, $(degree+1)$-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set.

### Fast and Simple Deterministic Algorithms for Highly-Dynamic Networks

- Computer ScienceArXiv
- 2019

A simple algorithm is presented, which handles multiple edge insertions/deletions while keeping the amortized round complexity at a small constant, and it is shown that the same approach can also fix labeling with large labels, given that they can be made to behave as small labels.

### Independent Sets of Dynamic Rectangles: Algorithms and Experiments

- Computer ScienceArXiv
- 2020

This work presents the first deterministic algorithm for maintaining a MIS (and thus a 4-approximate MAX-IS) of a dynamic set of uniform rectangles with amortized sub-logarithmic update time and establishes the trade-off between approximation quality and update time for synthetic and real-world map labeling data sets.

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This article significantly improves the update time for uniformly sparse graphs, and improves the result of Assadi et al. (at STOC’18) on maintaining a maximal independent set in a dynamic graph subject to edge insertions and deletions.

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