When the board of aldermen shall deem it necessary to pave, macadamize, gutter, curb (when such is set out in the street beyond the sidewalk) or otherwise improve any street, avenue, alley or other highway, or any part thereof, within the limits of the city for which a special tax is to be levied as herein provided, the board of aldermen shall, by resolution, declare the work or improvements necessary to be done, and cause the resolutions to be published in some newspaper published in the city for seven consecutive insertions in a daily paper or two consecutive insertions in a weekly paper. If a majority of the owners of the property liable to taxation therefor, residing in the city at the date of the passage of such resolution, shall not, within ten days from the date of the last insertion of the resolution, file with the city clerk their protest against, then the board of aldermen may cause the improvements to be made, and to contract therefor, and to levy the tax as herein provided. The findings of the board that a majority of such owners have not filed protest shall be conclusive and final. No publication shall be necessary for the making of any sidewalks, but upon the petition of any ten citizens of the city the board of aldermen may make contracts for the construction of sidewalks, including grading therefor, with or without curbing, along any street, avenue or other public highway, or any part thereof whatever. The contract shall be let to the lowest and best bidder, upon plans and specifications filed therefor by the city engineer or other officer designated by the board of aldermen, with the city clerk, not less than one week’s advertisement for bids thereupon being made in some newspaper published in the city. When upon proper advertisement no bid is received, the board of aldermen may proceed as provided in section 88.826.