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The metric k-median approximation threshold and recovery
Gives a deterministic polynomial-time -approximation for finite rational metric k-median with specified candidate facilities, for every fixed ε > 0. Assuming , the optimal infimum approximation factor is .
Manuscripts in this family · 2
Single-exponential recovery and bounded-price strictness for metric k-median
Sep 24, 2026·paper.pdfLean
We give an exact-budget recovery algorithm for metric k-median with single-exponential dependence on the number of comparison clusters without accurate, distinct proxies in a supplied anchor solution. On positive integral metrics of polynomially bounded diameter, a sufficiently small total proxy error and logarithmically many such clusters yield a approximation in polynomial time with arbitrarily high success probability. We also prove bounded-price strictness for one compatible execution of the logarithmic-surplus construction. Together the recovery and payment arguments give a randomized approximation, for an absolute σ > 0, on arbitrary finite rational metrics, both with high probability and in expectation, while opening at most k facilities on every output.
The approximation threshold for metric k-median
Sep 24, 2026·main.pdf
For every fixed ε > 0, we give a deterministic polynomial-time -approximation for finite rational metric k-median with specified candidate facilities, opening at most k facilities. Under , the infimum approximation factor in this model is therefore .