• Corpus ID: 237941199

# A (2+\epsilon)-Approximation Algorithm for Maximum Independent Set of Rectangles

@inproceedings{Galvez2021AA,
title={A (2+\epsilon)-Approximation Algorithm for Maximum Independent Set of Rectangles},
author={Waldo G'alvez and Arindam Khan and Mathieu Mari and Tobias Momke and Madhusudhan Reddy and Andreas Wiese},
year={2021}
}
• Published 1 June 2021
• Computer Science
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 [45] 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…

## References

SHOWING 1-10 OF 49 REFERENCES

### Approximating Maximum Independent Set for Rectangles in the Plane

• Joseph S. B. Mitchell
• Computer Science, Mathematics
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
• 2022
A polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane is given, based on a new form of recursive partitioning inThe plane, in which faces that are constant-complexity and orthogonally convex are recursively partitioned into a constant number of such faces.

### On Guillotine Separability of Squares and Rectangles

• Mathematics
APPROX-RANDOM
• 2020
It is shown that O(1)-fraction of rectangles, even in the weighted case, can be recovered for many special cases of Rectangles, e.g. fat (bounded width/height), δ-large (large in one of the dimensions), etc.

### Coloring and Maximum Weight Independent Set of Rectangles

• Mathematics, Computer Science
SODA
• 2021
The first asymptotic improvement over this six-decade-old bound is presented, proving that every intersection graph of axis-parallel rectangles in the plane admits an $O(\omega^2)$-coloring and presenting a polynomial-time algorithm that finds such a coloring.

### Polynomial-Time Approximation Schemes for Geometric Intersection Graphs

• Mathematics, Computer Science
SIAM J. Comput.
• 2005
These are the first known PTASs for $\mathcal{NP}$-hard optimization problems on disk graphs based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible.

### Approximation algorithms for maximum independent set of pseudo-disks

• Computer Science
SCG '09
• 2009
This work presents approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases, and suggests a novel rounding scheme based on an LP relaxation of the problem that leads to a constant-factor approximation.

### On guillotine cutting sequences. In Approximation, Randomization, and Combinatorial Optimization

• Algorithms and Techniques (APPROX/RANDOM),
• 2015

### Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More

• Computer Science, Mathematics
SoCG
• 2021
This paper gives (4/3 + ε)-approximation algorithms in polynomial time for both 2-Dimensional Knapsack problem and presents an algorithm that computes the essentially optimal structured packing into these regions.

### On Guillotine Separable Packings for the Two-dimensional Geometric Knapsack Problem

• Mathematics, Computer Science
SoCG
• 2021
A structural lemma is shown which shows that any guillotine packing can be converted into another structured guillsotine packing with almost the same profit, which might be useful for other settings where these constraints are imposed.

### A Tight (3/2+ε) Approximation for Skewed Strip Packing

• Computer Science
APPROX-RANDOM
• 2020
This work considers the complementary case where all the rectangles are skewed and provides an (almost) tight (3/2 + ε)-approximation algorithm for Strip Packing.

### Breaking the Barrier of 2 for the Storage Allocation Problem

• Computer Science, Mathematics
ICALP
• 2020
This paper breaks the barrier of 2 for the Storage Allocation Problem (SAP) which is a natural intermediate problem between 2DKP and UFP and presents a polynomial time (63/32) < 1.969-approximation algorithm for the case of uniform edge capacities and a quasi-polynomial time (1.997)-approximating algorithm for non-uniform quasi- polynomially bounded edge capacities.