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Bodlaender, Marijke H.L.; Halldórsson, Magnús M.; Konrad, Christian; Kühn, Fabian

doi:10.1145/2933057.2933068

Cited by 12 publications

References 11 publications

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Simple and Local Independent Set Approximation

Boppana

Halldórsson

Rawitz

2018

Structural Information and Communication Complexity

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We bound the performance guarantees that follow from Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as well as a streaming and preemptive online algorithm. We show it gives a tight (∆ + 1)/2-approximation in unweighted graphs of maximum degree ∆, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a ∆-approximation, but a simple modification results in an asymptotic expected 0.529∆-approximation. This compares with a recent, more complex ∆-approximation [5], which holds deterministically.

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Simple and Local Independent Set Approximation

Boppana

Halldórsson

Rawitz

2018

Structural Information and Communication Complexity

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Distributed Independent Sets in Interval and Segment Intersection Graphs

Gorain

Mondal

Pandit

2021

SOFSEM 2021: Theory and Practice of Computer Science

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The Maximal Independent Set problem is a well-studied problem in the distributed community. We study Maximum and Maximal Independent Set problems on two geometric intersection graphs; interval graphs and axis-parallel segment intersection graphs, and present deterministic distributed algorithms in the local communication model. We compute the maximum independent set on interval graphs in O(k) rounds and O(n) messages, where k is the size of the maximum independent set and n is the number of nodes in the graph. We provide a matching lower bound of Ω(k) on the number of rounds whereas Ω(n) is a trivial lower bound on message complexity. Thus our algorithm is both time and message optimal. We also study the maximal independent set problem in bi-interval graphs, a special case of the interval graphs where the intervals have two different lengths. We prove that a maximal independent set can be computed in bi-interval graphs in constant rounds that is 1 6 -approximation. For axis-parallel segment intersection graphs, we design an algorithm that finds a maximal independent set in O(D) rounds, where D is the diameter of the graph. We further show that this independent set is a 1 2 -approximation. The results in this paper extend the results of Molla et al. [J. Parallel Distrib. Comput. 2019].

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Distributed Fractional Local Ratio and Independent Set Approximation

Halldórsson,

Rawitz

2024

Lecture Notes in Computer Science

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Brief Announcement

Cited by 12 publications

References 11 publications

Simple and Local Independent Set Approximation

Simple and Local Independent Set Approximation

Distributed Independent Sets in Interval and Segment Intersection Graphs

Distributed Fractional Local Ratio and Independent Set Approximation

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