In the event that any owner, upon whose real estate or improvement thereof it is desired to take a lien under this article, should be a nonresident of this state, or in the event that any officer of this state authorized by law to execute legal process should make return "not found" upon any notice of a mechanic's lien which may be presented to him for service, then it shall be sufficient service of any such notice of mechanic's lien upon such nonresident owner, or upon such owner as to whom any such return, of "not found" shall be made by any such officer, to publish a copy of such notice as a Class II legal advertisement in compliance with the provisions of article three, chapter fifty-nine of this code, and the publication area for such publication shall be the county wherein the real estate lies. A copy of such notice shall also be posted in a conspicuous place upon the property sought to be charged thereby, which publishing and posting shall be sufficient, if commenced within the period provided by this article for the filing of such notice. The costs of such publication may be added to the account for which the lien is claimed, and, if included in the amount mentioned in the recorded notice, the lien shall cover such costs.