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### Geometry based heuristics for unit disk graphs

**1994-09-21**

9409226 | math.CO

Unit disk graphs are intersection graphs of circles of unit radius in the
plane. We present simple and provably good heuristics for a number of classical
NP-hard optimization problems on unit disk graphs. The problems considered
include maximum independent set, minimum vertex cover, minimum coloring and
minimum dominating set. We also present an on-line coloring heuristic which
achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not
need a geometric representation of unit disk graphs. Geometric representations
are used only in establishing the performance guarantees of the heuristics.
Several of our approximation algorithms can be extended to intersection graphs
of circles of arbitrary radii in the plane, intersection graphs of regular
polygons, and to intersection graphs of higher dimensional regular objects.

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