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

Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs