Emergent Mind
Complexity of Local Search for Euclidean Clustering Problems
(2312.14916)
Published Dec 22, 2023
in
cs.CC
and
cs.DS
Abstract
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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