Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Intersection graphs of segments
Journal of Combinatorial Theory Series B
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
Efficient approximation algorithms for tiling and packing problems with rectangles
Journal of 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
On the Approximation Properties of Independent Set Problem in Degree 3 Graphs
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Coloring kk-free intersection graphs of geometric objects in the plane
Proceedings of the twenty-fourth annual symposium on Computational geometry
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
A bipartite analogue of Dilworth's theorem for multiple partial orders
European Journal of Combinatorics
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The intersection graph of a set of geometric objects is defined as a graph G = (S, E) in which there is an edge between two nodes si, sj ∈ S if si ∩ sj ≠ 0. The problem of computing a maximum independent set in the intersection graph of a set of objects is known to be NP-complete for most cases in two and higher dimensions. We present approximation algorithms for computing a maximum independent set of intersection graphs of convex objects in R2. Specifically, given (i) a set of n line segments in the plane with maximum independent set of size α, we present algorithms that find an independent set of size at least (α/(2 log(2n/α)))1/2 in time O(n3) and (α/(2log(2n/α)))1/4 in time O(n4/3 logcn), (ii) a set of n convex objects with maximum independent set of size α, we present an algorithm that finds an independent set of size at least (α/(2log(2n/α)))1/3 in time O(n3 + τ (S)), assuming that S can be preprocessed in time τ(S) to answer certain primitive operations on these convex sets, and (iii) a set of n rectangles with maximum independent set of size βn, for β≤ 1, we present an algorithm that computes an independent set of size Ω (β2n). All our algorithms use the notion of partial orders that exploit the geometric structure of the convex objects.