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arXiv · 2605.03431

An Optimal Algorithm for Cardinality-Constrained Diameter Partitioning

Chao Xu·Mingdong Yang
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Abstract

Cardinality-constrained diameter partitioning asks for a partition of $n$ items into two classes of prescribed sizes that minimizes the larger of the two class diameters. We give an $O(n^2)$ algorithm and a matching $\Omega(n^2)$ lower bound if we can only query the weight between two elements. The algorithm computes the optimum for every cardinality simultaneously, improving Avis's $O(n^2\log n)$. The reduction is to a bottleneck 2-coloring problem on the maximum spanning tree, solved by a standard tree DP. For a single cardinality with Euclidean weights, we obtain a subquadratic time algorithm in any fixed dimension.

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Chao Xu, Mingdong Yang. 2026-05-05. An Optimal Algorithm for Cardinality-Constrained Diameter Partitioning. https://arxiv.org/abs/2605.03431

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