Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Discrete Mathematics - Topics on domination
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
An Expander-Based Approach to Geometric Optimization
SIAM Journal on Computing
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating Maximum Independent Sets by Excluding Subgraphs
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Approximating extent measures of points
Journal of the ACM (JACM)
Theory and application of width bounded geometric separators
Journal of Computer and System Sciences
Theory and application of width bounded geometric separator
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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Let S be a set of n points in R2. Given an integer 1 ≤ k ≤ n, we wish to find a maximally separated subset I ⊆ S of size k; this is a subset for which the minimum among the (k2) pairwise distances between its points is as large as possible. The decision problem associated with this problem is to determine whether there exists I ⊆ S, |I| = k, so that all (k2) pairwise distances in I are at least 2, say. This problem can also be formulated in terms of disk-intersection graphs: Let D be the set of unit disks centered at the points of S. The disk-intersection graph G of D connects pairs of disks by an edge if they have nonempty intersection. I is then the set of centers of disks that form an independent set in the graph G. This problem is known to be NP-Complete if k is part of the input.In this paper we first present a linear-time approximation algorithm for any constant k. Next we give O(n4/3polylog(n)) exact algorithms for the cases k = 3 and k = 4. We also present a simpler nO(√k)-time algorithm (as compared with the recent algorithm in [5]) for arbitrary values of k.