arXiv subjects

Mikhail Koshelev

Publications and source records attributed to Mikhail Koshelev.

2 recordsLinked to original sources

arXiv2026

Improved Approximations for Coflow Scheduling via Iterated Rounding and Stable Matchings

We study Coflow Scheduling, introduced by Chowdhury, Zhong, and Stoica (2014). We give deterministic polynomial-time algorithms achieving a $2.77$-approximation without release dates and a $3.17$-approximation with integer release dates. These improve the $3.42$ and $4.36$ guarantees of Rohwedder and Schnaars (2025). Our approach combines two ideas: (1) a novel iterated rounding scheme, and (2) Galvin's list edge coloring method, which is based on the Gale--Shapley stable matching algorithm.

cs.DS↗

arXiv2026

Ordinary and measurable colorings of Euclidean three-space

A proper coloring of Euclidean space is a coloring that assigns different colors to points at distance one. Using the planar character-law rigidity theorem of OpenAI, we prove that every finite proper coloring of $\R^3$ can be replaced by a proper Lebesgue-measurable coloring with the same number of colors. As a corollary we obtain that the ordinary and measurable chromatic numbers of $\R^3$ are equal, and both lie between $7$ and $15$.

math.CO↗