
Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time
We present the first algorithm for maintaining a maximal independent set...
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Dynamic Maximal Independent Set
Given a stream S of insertions and deletions of edges of an underlying g...
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Fully Dynamic Maximal Independent Set with Sublinear in n Update Time
The first fully dynamic algorithm for maintaining a maximal independent ...
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Dynamic Geometric Independent Set
We present fully dynamic approximation algorithms for the Maximum Indepe...
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Improved Algorithms for Fully Dynamic Maximal Independent Set
Maintaining maximal independent set in dynamic graph is a fundamental op...
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Maintaning maximal matching with lookahead
In this paper we study the problem of fully dynamic maximal matching wit...
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Learning Aggregation Functions
Learning on sets is increasingly gaining attention in the machine learni...
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Independent Sets of Dynamic Rectangles: Algorithms and Experiments
We study the maximal independent set (MIS) and maximum independent set (MAXIS) problems on dynamic sets of O(n) axisparallel rectangles, which can be modeled as dynamic rectangle intersection graphs. We consider the fully dynamic vertex update (insertion/deletion) model for two types of rectangles: (i) uniform height and width and (ii) uniform height and arbitrary width. These types of dynamic vertex update problems arise, e.g., in interactive map labeling. We present the first deterministic algorithm for maintaining a MIS (and thus a 4approximate MAXIS) of a dynamic set of uniform rectangles with amortized sublogarithmic update time. This breaks the natural barrier of O(Δ) update time (where Δ is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018). We continue by investigating MAXIS and provide a series of deterministic dynamic approximation schemes. For uniform rectangles, we first give an algorithm that maintains a 4approximate MAXIS with O(1) update time. In a subsequent algorithm, we establish the tradeoff between approximation quality 2(1+1/k) and update time O(k^2log n) for k∈ℕ. We conclude with an algorithm that maintains a 2approximate MAXIS for dynamic sets of uniform height and arbitrary width rectangles with O(ωlog n) update time, where ω is the largest number of maximal cliques stabbed by any axisparallel line. We have implemented our algorithms and report the results of an experimental comparison exploring the tradeoff between solution size and update time for synthetic and realworld map labeling data sets.
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