We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only near-linear total work and finishing in polylog time. The algorithms compute $(1+epsilon)$-approximate solutions in time (and work) $O^*(N/epsilon^2)$, where $N$ is the number of non-zeros in the constraint matrix. For facility location, $N$ is the number of eligible client/facility pairs.
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