In all cases where the governing body of any city with a population of over ten thousand has heretofore entered into an agreement with the department of transportation of the state of North Dakota for the improvement of streets and construction of street lights, sewers, water mains or any of such facilities, and for such purpose has created a special improvement district or districts and has by resolution declared the necessity of such improvement, whether or not final plans and specifications for such work and estimates of the cost thereof have previously been prepared and filed, and has caused such resolution to be published in the official newspaper of the city, and no protests have been filed with the city auditor within thirty days after the first publication of such resolution by owners of property situated within the improvement district, or    the protests so filed are signed by owners of less than seventy-five percent of such property, all such proceedings are hereby legalized and validated, notwithstanding any errors, omissions or defects therein, including, but without limitation, any defect which exists or may exist by reason of the execution of any such agreement and the award of a contract for construction of all or any part of any such improvement by the city or the department of transportation prior to the adoption of and hearing of protests against the resolution of necessity, and any and all such agreements and contracts heretofore entered into are likewise legalized and validated, and such cities are hereby authorized to pay all or any part of their share of the cost of any such improvement by the levy of special assessments upon benefited properties within the improvement district created therefor, or by the levy of ad valorem taxes upon all taxable property within their corporate limits, or by both of such means, in the manner prescribed in title 40, provided that in no case may the principal sum be paid initially by the levy of ad valorem taxes exceed twenty percent of the total cost of any such improvement, and such cities are further authorized to issue warrants in anticipation of the collection of such special assessments and taxes and to take all measures for the collection of said assessments and taxes and the payment of said warrants as are provided in said title 40.