Adrian Dumitrescu
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چکیده
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 in F? (II) The following question was asked by Erdős 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?
منابع مشابه
Binary Space Partitions
Binary Space Partitions Name: Adrian Dumitrescu, Csaba D. Tóth Affil./Addr. 1: Computer Science, Univ. of Wisconsin–Milwaukee, Milwaukee, WI, USA Affil./Addr. 2: Mathematics, California State University Northridge, Los Angeles, CA, USA Affil./Addr. 3: Computer Science, Tufts University, Medford, MA, USA
متن کامل53 Adrian Dumitrescu
This column is devoted to partitions of point-sets into convex subsets with interior-disjoint convex hulls. We review some partitioning problems and corresponding algorithms. At the end we list some open problems. For simplicity, in most cases we remain at the lowest possible interesting level, that is, in the plane.
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تاریخ انتشار 2013