Whenever any person, persons, firm, association or corporation interested in any city which if incorporated is not exercising its corporate functions may desire to vacate any lot, tract, private road, common, plot or any part thereof in any such city, it shall be lawful to petition the board of county commissioners of the county where such property is located, setting forth the particular circumstances of the case, and giving a distinct description of the property to be vacated and the names of the persons to be particularly affected thereby; which petition shall be filed with the appropriate county or highway district clerk and notice of the pendency of said petition shall be given for a period of thirty (30) days by written notice thereof, containing a description of the property to be vacated, posted in three (3) public or conspicuous places in said city, and also within the limits of said platted acreage, or in the event such property is located within a county in which there is published a newspaper, as defined by law, such notice shall also be published in such newspaper, once a week for two (2) successive weeks. Provided however, when a public street or public right-of-way is located within the boundary of a highway district or is under the jurisdiction of a county, the respective commissioners of the highway district or board of county commissioners shall assume the authority to vacate said public street or public right-of-way pursuant to section 40-203, Idaho Code. Land exclusive of public right-of-way that has been subdivided and platted in accordance with this chapter need not be vacated in order to be replatted.