A study on two geometric location problems
Information Processing Letters
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
On the efficiency of polynomial time approximation schemes
Information Processing Letters
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of 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
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Refined memorization for vertex cover
Information Processing Letters
Parameterized Complexity
On the parameterized complexity of d-dimensional point set pattern matching
Information Processing Letters
Geometric clustering: fixed-parameter tractability and lower bounds with respect to the dimension
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
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
Geometric clustering: Fixed-parameter tractability and lower bounds with respect to the dimension
ACM Transactions on Algorithms (TALG)
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Polynomial kernels for hard problems on disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Parameterized complexity of independence and domination on geometric graphs
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On the parameterized complexity of d-dimensional point set pattern matching
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Safe approximation and its relation to kernelization
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
Parameterized complexity of induced h-matching on claw-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On approximating string selection problems with outliers
Theoretical Computer Science
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An EPTAS (efficient PTAS) is an approximation scheme where ε does not appear in the exponent of n, i.e., the running time is f(ε)nc. We use parameterized complexity to investigate the possibility of improving the known approximation schemes for certain geometric problems to EPTAS. Answering an open question of Alber and Fiala [2], we show that Maximum Independent Set is W[1]-complete for the intersection graphs of unit disks and axis-parallel unit squares in the plane. A standard consequence of this result is that the $n^{O(1/{\it \epsilon})}$ time PTAS of Hunt et al. [11] for Maximum Independent Set on unit disk graphs cannot be improved to an EPTAS. Similar results are obtained for the problem of covering points with squares.