The board of supervisors to whom the petition is addressed, at its next regular meeting shall set the time and place when it shall meet for a hearing on the petition, and it shall direct the county auditor in whose office the petition is filed to cause notice to be given to all persons whom it may concern, without naming them, of the pendency and request of the petition for the conveyance and discontinuance by publication of a notice as provided in section 331.305. Proof of giving notice shall be made by affidavit of the publisher and shall be filed with the county auditor at the time the hearing begins.