## NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs (1997)

Citations: | 93 - 1 self |

### BibTeX

@MISC{Hunt97nc-approximationschemes,

author = {Harry B. Hunt and III and Madhav V. Marathe and VENKATESH RADHAKRISHNAN and S. S. Ravi and Daniel J. Rosenkrantz and Richard E. Stearns},

title = {NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance trade-off as the best known approximation schemes for planar graphs. We also define the concept of -precision unit disk graphs and show that for such graphs the approximation schemes have a better time versus performance trade-off than the approximation schemes for arbitrary unit disk graphs. Moreover, compared to unit disk graphs, we show that for -precision unit disk graphs, many more graph problems have efficient approximation schemes. Our NC approximation schemes can also be extended to obtain efficient NC approximation schemes for several PSPACE-hard problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann and Widmayer. The approximation schemes for hierarchically specified un...