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A rule-based system for dense-map name placement
Communications of the ACM
A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
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
Resource sharing in advance reservation agents
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On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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Theoretical Computer Science
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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ACM Transactions on Database Systems (TODS)
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Journal of the ACM (JACM)
ICDE '97 Proceedings of the Thirteenth International Conference on Data Engineering
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APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
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BC '98 Proceedings of the IFIP TC6/WG6.2 Fourth International Conference on Broadband Communications: The future of telecommunications
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
A note on maximum independent set and related problems on box graphs
Information Processing Letters
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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SIAM Journal on Computing
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ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
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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
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Computational Geometry: Theory and Applications
Approximation algorithms for free-label maximization
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
Proceedings of the twenty-eighth annual symposium on Computational geometry
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
Optimization problems in dotted interval graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Constant integrality gap LP formulations of unsplittable flow on a path
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve
Computational Geometry: Theory and Applications
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We study the Maximum Independent Set of Rectangles (MISR) problem: given a collection R of n axis-parallel rectangles, find a maximum-cardinality subset of disjoint rectangles. MISR is a special case of the classical Maximum Independent Set problem, where the input is restricted to intersection graphs of axis-parallel rectangles. Due to its many applications, ranging from map labeling to data mining, MISR has received a significant amount of attention from various research communities. Since the problem is NP-hard, the main focus has been on the design of approximation algorithms. Several groups of researches have independently suggested O(log n)-approximation algorithms for MISR, and this remained the best currently known approximation factor for the problem. The main result of our paper is an O(log log n)-approximation algorithm for MISR. Our algorithm combines existing approaches for solving special cases of the problem, in which the input set of rectangles is restricted to containing specific intersection types, with new insights into the combinatorial structure of sets of intersecting rectangles in the plane. We also consider a generalization of MISR to higher dimensions, where rectangles are replaced by d-dimensional hyper-rectangles. Our results for MISR imply an O((log n)d−2 log log n)-approximation algorithm for this problem, improving upon the best previously known O((log n)d−1)-approximation.