First poly-time algorithms for matroid-intersection coloring achieve a 2-approximation for two matroids and (k^2-k) approximation for k matroids, plus an FPRAS for asymptotic Rota's Basis Conjecture.
Marilena Leichter, Benjamin Moseley, and Kirk Pruhs
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Approximation Algorithms for Matroid-Intersection Coloring with Applications to Rota's Basis Conjecture
First poly-time algorithms for matroid-intersection coloring achieve a 2-approximation for two matroids and (k^2-k) approximation for k matroids, plus an FPRAS for asymptotic Rota's Basis Conjecture.