The Dynamic Vertex Minimum Problem and Its Application to Clustering-Type Approximation Algorithms

@inproceedings{Gabow2002TheDV,
  title={The Dynamic Vertex Minimum Problem and Its Application to Clustering-Type Approximation Algorithms},
  author={Harold N. Gabow and Seth Pettie},
  booktitle={SWAT},
  year={2002}
}
The dynamic vertex minimum problem (DVMP) is to maintain the minimum cost edge in a graph that is subject to vertex additions and deletions. DVMP abstracts the clustering operation that is used in the primal-dual approximation scheme of Goemans and Williamson (GW). We present an algorithm for DVMP that immediately leads to the best-known time bounds for the GW approximation algorithm for problems that require a metric space. These bounds include time O(n) for the prize-collecting TSP and other… CONTINUE READING
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