Senatorial district meetings, representative district meetings, and voting district meetings for the purposes of election shall be warned and organized as is or may be provided by law, and notice of all these meetings shall be given by the city or town clerk issuing his or her warrant, directed to the town sergeant or one of the constables of that city or town, or in the event that the town sergeant or a constable is not available, to any member of the town or city clerk’s office or member of the board of canvassers, directing him or her to post, at least seven (7) days before the day appointed for these meetings, written notifications in one or more public places in each voting district, and in each senatorial and representative district not divided into voting districts, of the time when, and place where, each meeting is to be held, and of the business required by law to be transacted in the meeting, and stating in the warrant the time of the opening and closing of the polls at each elective meeting to be held in that city or town; provided, that the local boards may, at their discretion, substitute notification by publication in a newspaper having local circulation for notification by posting in public places; and further provided, that in the cities of Providence, Pawtucket, Central Falls, Newport, Cranston, Warwick, and Woonsocket, the notice shall be given and posted by the local board.