Hierarchically Specified Unit Disk Graphs

We characterize the complexity of a number of basic optimization problems for unit disk graphs speciied hierarchically as in BOW83, LW87a, Le88, LW92]. Both PSPACE-hardness results and polynomial time approximations are presented for most of the problems considered. These problems include minimum vertex coloring, maximum independent set, minimum clique cover, minimum dominating set and minimum independent dominating set. Each of our PSPACE-hardness results holds, when the hierarchical speciications are 1-level restricted and the graphs are speciied hierarchically either as in BOW83] or as in LW92]. The hardness results presented here signiicantly extend the hardness results in BOW83, LW92]. The approximation algorithms presented here along with our results in MHR93, MHSR94] are among the rst polynomial time approximation algorithms for natural PSPACE-hard functions.