When the legislative body of any city or town finds that all of the property within a local improvement district or utility local improvement district will be benefited by the improvements as a whole, a local improvement district or utility local improvement district may include adjoining, vicinal, or neighboring streets, avenues, and alleys or other improvements even though the improvements thus made are not connected or continuous. The assessment rates may be ascertained on the basis of the special benefit of the improvements as a whole to the properties within the entire local improvement district or utility local improvement district, or on the basis of the benefit of each unit of the improvements to the properties specially benefited by that unit, or the assessment rates may be ascertained by a combination of the two bases. Where no finding is made by the legislative body as to the benefit of the improvements as a whole to all of the property within a local improvement district or utility local improvement district, the cost and expense of each continuous unit of the improvements shall be ascertained separately, as near as may be, and the assessment rates shall be computed on the basis of the cost and expense of each unit. In the event of the initiation of a local improvement district authorized by this section or a utility local improvement district authorized by this section, the legislative body may, in its discretion, eliminate from the district any unit of the improvement which is not connected or continuous and may proceed with the balance of the improvement within the local improvement district or utility local improvement district, as fully and completely as though the eliminated unit had not been included within the improvement district, without the giving of any notices to the property owners remaining within the district, other than such notices as are required by the provisions of this chapter to be given subsequent to such elimination.