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 Erdos 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?
['Adrian Dumitrescu', 'Minghui Jiang']
Computational geometry column 56