A city is authorized without petition to order any of the improvements specified in section 14-385 within street improvement districts, mall improvement districts, separate or combined street and sidewalk, or street, or sidewalk, or streets and sidewalks improvement districts within the corporate limits of the city or when the improvement is on a controlled-access facility or a major traffic street contained in the approved master plan of the city, and on sidestreets connecting with such major traffic streets for a distance not to exceed one block from such major traffic street.