@inproceedings{64b25d79feec4f619ce6d99c8d36410c,
title = "Distributed Independent Sets in Interval and Segment Intersection Graphs",
abstract = "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 16 -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 12 -approximation. The results in this paper extend the results of Molla et al. [J. Parallel Distrib. Comput. 2019].",
keywords = "Approximation algorithm, Distributed algorithm, Interval graph, Maximal Independent Set, Segment intersection graph",
author = "Barun Gorain and Kaushik Mondal and Supantha Pandit",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021 ; Conference date: 25-01-2021 Through 29-01-2021",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-67731-2_13",
language = "English",
isbn = "9783030677305",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "175--188",
editor = "Tom{\'a}{\v s} Bure{\v s} and Riccardo Dondi and Johann Gamper and Giovanna Guerrini and Tomasz Jurdzinski and Claus Pahl and Florian Sikora and Wong, {Prudence W.}",
booktitle = "SOFSEM 2021",
address = "Germany",
}