SIAM Journal on Discrete Mathematics
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)
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
On the algorithmic complexity of twelve covering and independence parameters of graphs
Discrete Applied Mathematics
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast stabbing of boxes in high dimensions
Theoretical Computer Science
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Efficient approximation algorithms for tiling and packing problems with rectangles
Journal of Algorithms
Simple approximation algorithm for nonoverlapping local alignments
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
Routing and Admission Control in Networks with Advance Reservations
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Bipartite Domination and Simultaneous Matroid Covers
SIAM Journal on Discrete Mathematics
Approximability results for stable marriage problems with ties
Theoretical Computer Science
Approximating the Maximum Independent Set and Minimum Vertex Coloring on Box Graphs
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
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The MAXIMUM INDEPENDENT SET problem in d-box graphs, i.e., in the intersection graphs of axis-parallel rectangles in Rd, is a challenge open problem. For any fixed d ≥ 2 the problem is NP-hard and no approximation algorithm with ratio o(logd-1 n) is known. In some restricted cases, e.g., for d-boxes with bounded aspect ratio, a PTAS exists [17]. In this paper we prove APX-hardness (and hence non-existence of a PTAS, unless P = NP), of the MAXIMUM INDEPENDENT SET problem in d-box graphs for any fixed d ≥ 3. We state also first explicit lower bound 443/442 on efficient approximability in such case. Additionally, we provide a generic method how to prove APX-hardness for many NP-hard graph optimization problems in d-box graphs for any fixed d ≥ 3. In 2-dimensional case we give a generic approach to NP-hardness results for these problems in highly restricted intersection graphs of axis-parallel unit squares (alternatively, in unit disk graphs).