Abstract
A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric representation (specifying the coordinates of the disk centers).
The approximation algorithm presented is robust in the sense that it accepts any graph as input and either returns a (1+ε)-approximate independent set or a certificate showing that the input graph is no unit disk graph. The algorithm can easily be extended to other families of intersection graphs of geometric objects.
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Nieberg, T., Hurink, J., Kern, W. (2004). A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_18
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DOI: https://doi.org/10.1007/978-3-540-30559-0_18
Publisher Name: Springer, Berlin, Heidelberg
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