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We give almost-linear-time algorithms for constructing sparsifiers with n poly(log n) edges that approximately preserve weighted (𝓁²₂ + 𝓁^p_p) flow or voltage objectives on graphs. For flow objectives, this is the first sparsifier construction for such mixed objectives beyond unit 𝓁_p weights, and is based on expander decompositions. For voltage objectives, we give the first sparsifier construction for these objectives, which we build using graph spanners and leverage score sampling. Togetherdoi:10.4230/lipics.icalp.2021.9 fatcat:wxtvuhv6t5chfcvbdwqumiymy4