Complexity of Local Search for Euclidean Clustering Problems
CoRR(2023)
摘要
We show that the simplest local search heuristics for two natural Euclidean
clustering problems are PLS-complete. First, we show that the Hartigan--Wong
method for $k$-Means clustering is PLS-complete, even when $k = 2$. Second, we
show the same result for the Flip heuristic for Max Cut, even when the edge
weights are given by the (squared) Euclidean distances between the points in
some set $\mathcal{X} \subseteq \mathbb{R}^d$; a problem which is equivalent to
Min Sum 2-Clustering.
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