Ulam Metric \(k\)-Center in Parameterized Linear Time

Source: hexagonmath.org/abs/2611.00055v1

Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník

Hexagonhexagon/2611.00055Nov 4, 2026cs.DSAI-generatedscore 0

Continuous Ulam Metric \(k\)-Center asks for at most \(k\) permutations whose radius-\(d\) balls cover the input rankings. For \(m\) rankings of \(n\) symbols, a deterministic algorithm takes \(2^{O(kd\log(k+d+2))}mn\) word operations. Permanent reference rankings, short insertion lists, and small obstructions obtained by patience sorting control the search. For one center, this answers a question of Bai, Fomin, Golovach, More, and Wietheger with linear input dependence. An arbitrary-alphabet Hamming embedding with a nonexpansive retraction also gives the matching \(2^{o(d\log d)}\)…

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