Computational geometry column 56

Authors:
Adrian Dumitrescu;Minghui Jiang
Affiliations:
Department of Computer Science, University of Wisconsin--Milwaukee, USA;Department of Computer Science, Utah State University, Logan, USA
Venue:
ACM SIGACT News
Year:
2013

Citing 6
Cited 0

Unit disk graphs

Discrete Mathematics - Topics on domination
Polynomial-time approximation schemes for packing and piercing fat objects

Journal of Algorithms
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs

SIAM Journal on Computing
On Covering Problems of Rado

Algorithmica - Special Issue: Scandinavian Workshop on Algorithm Theory; Guest Editor: Joachim Gudmundsson
Piercing Translates and Homothets of a Convex Body

Algorithmica - Special Issue: European Symposium on Algorithms, Design and Analysis
Systems of distant representatives in euclidean space

Proceedings of the twenty-ninth annual symposium on Computational geometry

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Abstract

This column is devoted to maximum (respectively, maximum weight) independent set problems in geometric intersection graphs. We illustrate with one example in each class: (I) The following question was asked by T. Rado in 1928: What is the largest number c such that, for any finite set F of axis-parallel squares in the plane, there exists an independent subset I ⊆ F of pairwise disjoint squares with total area at least c times the union area of the squares. (II) The following question was asked by Erdös in 1983: What is the largest number H = H(n) with the property that every set of n non-overlapping unit disks in the plane has an independent subset with at least H members?