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Roughly a year before the fatal shooting rampage at Los Angeles International Airport, federal security officials turned away a request by the head of the local airport-police union to ensure armed security was posted around screening checkpoints.

The request highlighted a debate that has been reignited by Friday’s shooting: Whether armed officers should be present at airport security-screening stations nationwide. Such an armed presence was commonplace after the 2001 terrorist attacks, but it gradually disappeared in the face of cost concerns and changing priorities.