Approximation algorithms for maximum independent set of pseudo-disks

Authors:
Timothy M. Chan;Sariel Har-Peled
Affiliations:
University of Waterloo/ 200, Waterloo,, ON, Canada;UIUC, Urbana, IL, USA
Venue:
Proceedings of the twenty-fifth annual symposium on Computational geometry
Year:
2009

Citing 21
Cited 16

On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles

Discrete & Computational Geometry
Fast algorithms for shortest paths in planar graphs, with applications

SIAM Journal on Computing
Applications of random sampling in computational geometry, II

Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Approximation algorithms for NP-complete problems on planar graphs

Journal of the ACM (JACM)
Randomized algorithms

Randomized algorithms
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems

Journal of the ACM (JACM)
Label placement by maximum independent set in rectangles

WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Dynamic data structures for fat objects and their applications

Computational Geometry: Theory and Applications
Efficient approximation algorithms for tiling and packing problems with rectangles

Journal of Algorithms
Approximations of Independent Sets in Graphs

APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Polynomial-time approximation schemes for packing and piercing fat objects

Journal of Algorithms
Geometric Separator Theorems and Applications

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs

SIAM Journal on Computing
Hitting sets when the VC-dimension is small

Information Processing Letters
Independent set of intersection graphs of convex objects in 2D

Computational Geometry: Theory and Applications
Improved Approximation Algorithms for Geometric Set Cover

Discrete & Computational Geometry
Dynamic connectivity for axis-parallel rectangles

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Beating Simplex for Fractional Packing and Covering Linear Programs

FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
New existence proofs ε-nets

Proceedings of the twenty-fourth annual symposium on Computational geometry
Maximum independent set of rectangles

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A robust PTAS for maximum weight independent sets in unit disk graphs

WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science

PTAS for geometric hitting set problems via local search

Proceedings of the twenty-fifth annual symposium on Computational geometry
An Approximation Scheme for Terrain Guarding

APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Shifting Strategy for Geometric Graphs without Geometry

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Weighted geometric set cover via quasi-uniform sampling

Proceedings of the forty-second ACM symposium on Theory of computing
Algorithms for dominating set in disk graphs: breaking the log n Barrier

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimum vertex cover in rectangle graphs

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimum vertex cover in rectangle graphs

Computational Geometry: Theory and Applications
Submodular function maximization via the multilinear relaxation and contention resolution schemes

Proceedings of the forty-third annual ACM symposium on Theory of computing
Coloring and maximum independent set of rectangles

APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On isolating points using disks

ESA'11 Proceedings of the 19th European conference on Algorithms
Polynomial kernels for hard problems on disk graphs

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Geometric packing under non-uniform constraints

Proceedings of the twenty-eighth annual symposium on Computational geometry
Conflict-free coloring of points with respect to rectangles and approximation algorithms for discrete independent set

Proceedings of the twenty-eighth annual symposium on Computational geometry
Shifting strategy for geometric graphs without geometry

Journal of Combinatorial Optimization
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve

Computational Geometry: Theory and Applications
Exact algorithms and APX-hardness results for geometric packing and covering problems

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a PTAS. For the weighted case, we suggest a novel rounding scheme based on an LP relaxation of the problem, that leads to a constant-factor approximation. Most previous algorithms for maximum independent set (in geometric settings) relied on packing arguments that are not applicable in this case. As such, the analysis of both algorithms requires some new combinatorial ideas, which we believe to be of independent interest.