A Simple Polynomial Time Algorithm for Max Cut on Laminar Geometric Intersection Graphs

Joshi, U and Rahul, S and Thoppil, JJ (2022) A Simple Polynomial Time Algorithm for Max Cut on Laminar Geometric Intersection Graphs. In: Leibniz International Proceedings in Informatics, LIPIcs, 18 - 20 December 2022, Chennai.

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Abstract

In a geometric intersection graph, given a collection of n geometric objects as input, each object corresponds to a vertex and there is an edge between two vertices if and only if the corresponding objects intersect. In this work, we present a somewhat surprising result: a polynomial time algorithm for max cut on laminar geometric intersection graphs. In a laminar geometric intersection graph, if two objects intersect, then one of them will completely lie inside the other. To the best of our knowledge, for max cut this is the first class of (non-trivial) geometric intersection graphs with an exact solution in polynomial time. Our algorithm uses a simple greedy strategy. However, proving its correctness requires non-trivial ideas. Next, we design almost-linear time algorithms (in terms of n) for laminar axis-aligned boxes by combining the properties of laminar objects with vertical ray shooting data structures. Note that the edge-set of the graph is not explicitly given as input; only the n geometric objects are given as input. © Utkarsh Joshi, Saladi Rahul, and Josson Joe Thoppil; licensed under Creative Commons License CC-BY 4.0.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords:	Clustering algorithms; Graph theory; Graphic methods; Polynomial approximation, Exact solution; Geometric intersection graphs; Geometric objects; MAX CUT; Max-cut; Non-trivial; Polynomial-time algorithms; Ray shooting; Simple++; Vertical ray shooting, Geometry
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	27 Jan 2023 09:49
Last Modified:	27 Jan 2023 09:49
URI:	https://eprints.iisc.ac.in/id/eprint/79564

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