"given the approaching" is correct and usable in written English.
You can use it when you want to indicate that something will soon happen or be available. For example, "Given the approaching holiday season, stores are already stocking up on toys and decorations."
However, given the approaching deadline, a move to Villa now seems the likeliest.
The F.B.I. data are particularly grim given the approaching anniversary of the shooting rampage in Tucson that left Representative Gabrielle Giffords gravely shot in the head, six people dead, including a federal judge, and 13 others wounded.
Moving forward, however, it may get trickier for McConnell to continue with regular order, given the approaching deadlines on the debt limit, highway funding and more.
Then again, given the approach to language in this campaign, who knows what Romney means?
An executive close to Enron described the loan extension, by J. P. Morgan Chase and Citigroup, as a Band-Aid, given the approach of Thanksgiving.
Given the approach of numerical simulation, a sensitivity analysis for all parameters was carried out, which specifically demonstrated that initial temperature is the most important parameter.
That is, it is an important reminder from the pontiff, and an especially timely one, given the approach of Passover and Easter.
The participants were given the Approaches and Study Skills Inventory for Students (ASSIST) questionnaire.
Given the approach taken in prior MESA analyses (which have not used multiple imputation), we report results based on participants with complete data.
Self-stability is the most important dynamic feature of any reactors, and analyzing the self-stability can give the approach of improving the operation performance.
The relationship between discharge and approach-flow head loss should theoretically be linear and the regression coefficient gives the approach-flow resistance.
