Cities are empowered to cause all sidewalks and alleys to be cleared of snow, ice and rubbish, and the cutting and removal of trees, weeds and grass, and the removal of rubbish upon and from all private property within the city and the parking within the curbing abutting same, and to assess the cost thereof against the private property so cleared, and against the property abutting the parking, sidewalks and alleys so cleaned. Such assessment shall be collected as provided in section 50-1008.