{"id":"hexagon/2611.00055","pdf":"https://hexagonmath.org/pdf/2611.00055v1","url":"https://hexagonmath.org/abs/2611.00055v1","tags":["cs.CC","math.CO","msc:68Q27","msc:05A05","msc:68R15","Exponential Time Hypothesis","Ulam distance","continuous k-center","parameterized algorithms","patience sorting"],"score":0,"title":"Ulam Metric \\(k\\)-Center in Parameterized Linear Time","domain":"cs.DS","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"cs.DS","summary":"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)}\\)…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}