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