A 3-Approximation Algorithm for Maximum Independent Set of Rectangles

Galvez, W and Khan, A and Mari, M and Mömke, T and Pittu, MR and Wiese, A (2022) A 3-Approximation Algorithm for Maximum Independent Set of Rectangles. In: 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, 9 January 2022 through 12 January 2022, Alexander, pp. 894-905.

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Abstract

We study the Maximum Independent Set of Rectangles (MISR) problem, where we are given a set of axis-parallel rectangles in the plane and the goal is to select a subset of non-overlapping rectangles of maximum cardinality. In a recent breakthrough, Mitchell 46 obtained the first constant-factor approximation algorithm for MISR. His algorithm achieves an approximation ratio of 10 and it is based on a dynamic program that intuitively recursively partitions the input plane into special polygons called corner-clipped rectangles (CCRs), without intersecting certain special horizontal line segments called fences. In this paper, we present a 3-approximation algorithm for MISR which is also based on a recursive partitioning scheme. First, we use a partition into a class of axis-parallel polygons with constant complexity each that are more general than CCRs. This allows us to provide an arguably simpler analysis and at the same time already improves the approximation ratio to 6. Then, using a more elaborate charging scheme and a recursive partitioning into general axis-parallel polygons with constant complexity, we improve our approximation ratio to 3. In particular, we construct a recursive partitioning based on more general fences which can be sequences of up to O(1) line segments each. This partitioning routine and our other new ideas may be useful for future work towards a PTAS for MISR.

Item Type:	Conference Paper
Publication:	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher:	Association for Computing Machinery
Additional Information:	The copyright for this article belongs to the SIAM, Association for Computing Machinery
Keywords:	Approximation algorithms; Fences; Set theory, Approximation ratios; Axis parallel rectangles; Cardinalities; Constant-factor approximation algorithms; Dynamic programs; Input planes; Line-segments; Maximum independent sets; Recursive Partitioning; Simple analysis, Geometry
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	06 Jul 2022 05:16
Last Modified:	06 Jul 2022 05:16
URI:	https://eprints.iisc.ac.in/id/eprint/74153

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