Fully dynamic maximal independent set with sublinear update time

Assadi, Sepehr; Onak, Krzysztof; Schieber, Baruch; Solomon, Shay

doi:10.1145/3188745.3188922

Cited by 48 publications

(80 citation statements)

References 60 publications

(88 reference statements)

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Section: Our Contributionmentioning

confidence: 99%

“…We focus on graphs that are "uniformly sparse" or "sparse everywhere", as opposed to the previous work by Assadi et al [2] that considers unrestricted sparse graphs. We aim to improve the update time of [2] as a function of the "uniform sparsity" of the graph. This fundamental property of graphs has been studied in various contexts and under various names over the years, one of which is arboricity [19,20,23]:…”

Section: Our Contributionmentioning

confidence: 99%

“…In STOC'18, Assadi, Onak, Schieber, and Solomon [2] gave the first fully dynamic algorithm for maintaining an MIS with sub-linear (amortized) update time. Their update time is min{m 3/4 , ∆}, where m is the (dynamically changing) number of edges and ∆ is a fixed bound on the maximum degree of the graph.…”

Section: Introductionmentioning

confidence: 99%

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Fully Dynamic MIS in Uniformly Sparse Graphs

Onak

Schieber

Solomon

et al. 2020

ACM Trans. Algorithms

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We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear (in the dynamically changing number of edges) amortized update time. In this paper 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(α 2 · log 2 n), where n is the number of vertices. For low arboricity graphs, which include, for example, minor-free graphs as well as 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−ǫ , for any constant ǫ > 0. This covers much of the range of possible values for arboricity, as the arboricity of a general graph cannot exceed m 1/2 . * A preliminary version of this paper appeared in the proceedings of ICALP'18.

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Section: Our Contributionmentioning

confidence: 99%

Section: Our Contributionmentioning

confidence: 99%

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Fully Dynamic MIS in Uniformly Sparse Graphs

Onak

Schieber

Solomon

et al. 2020

ACM Trans. Algorithms

Self Cite

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“…// Initialized in the pre-processing step. 3 while S is not empty do 4 Let v ← arg min u∈S π(u) be the minimum rank vertex in S. 5 if…”

Section: The Algorithmmentioning

confidence: 99%

Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time

Behnezhad

Derakhshan

Hajiaghayi

et al. 2019

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

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We present 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. Our algorithm is randomized and, per update, takes O(log 2 ∆ · log 2 n) expected time. Furthermore, the algorithm can be adjusted to have O(log 2 ∆ · log 4 n) worst-case update-time with high probability. Here, n denotes the number of vertices and ∆ is the maximum degree in the graph. The MIS problem in fully dynamic graphs has attracted significant attention after a breakthrough result of Assadi, Onak, Schieber, and Solomon [STOC'18] who presented an algorithm with O(m 3/4 ) update-time (and thus broke the natural Ω(m) barrier) where m denotes the number of edges in the graph. This result was improved in a series of subsequent papers, though, the update-time remained polynomial. In particular, the fastest algorithm prior to our work had O(min{ √ n, m 1/3 }) update-time [Assadi et al. SODA'19].Our algorithm maintains the lexicographically first MIS over a random order of the vertices. As a result, the same algorithm also maintains a 3-approximation of correlation clustering. We also show that a simpler variant of our algorithm can be used to maintain a random-order lexicographically first maximal matching in the same update-time. * A preliminary version of this paper is

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“…Since KAMIS currently does not support weighted instances, prioritizing labels of a previous solution via weights is not possible with KAMIS. From a theoretical perspective, specialized algorithms that respect a previous solution have been considered recently for the dynamic independent set problem [4]. So far, this was not investigated in the light of the PFLP problem.…”

Section: Labeling Algorithmsmentioning

confidence: 99%

Exploring Semi-Automatic Map Labeling

Klute

Löffler

et al. 2019

Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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Label placement in maps is a very challenging task that is critical for the overall map quality. Most previous work focused on designing and implementing fully automatic solutions, but the resulting visual and aesthetic quality has not reached the same level of sophistication that skilled human cartographers achieve. We investigate a different strategy that combines the strengths of humans and algorithms. In our proposed method, first an initial labeling is computed that has many well-placed labels but is not claiming to be perfect. Instead it serves as a starting point for an expert user who can then interactively and locally modify the labeling where necessary. In an iterative human-in-the-loop process alternating between user modifications and local algorithmic updates and refinements the labeling can be tuned to the user's needs.We demonstrate our approach by performing different possible modification steps in a sample workflow with a prototypical interactive labeling editor. Further, we report computational performance results from a simulation experiment in QGIS, which investigates the differences between exact and heuristic algorithms for semi-automatic map labeling. To that end, we compare several alternatives for recomputing the labeling after local modifications and updates, as a major ingredient for an interactive labeling editor.

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Fully dynamic maximal independent set with sublinear update time

Cited by 48 publications

References 60 publications

Fully Dynamic MIS in Uniformly Sparse Graphs

Fully Dynamic MIS in Uniformly Sparse Graphs

Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time

Exploring Semi-Automatic Map Labeling

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