Hawaii Revised Statutes Division 3. Property; Family § 578-7

(1) Personal service or service by registered mail without the State. If the residence of a nonresident legal parent is known or is ascertained at any stage of the proceeding prior to the filing of a return of service pursuant to section 578-5, the court may order that service of notice of the time and place of hearing of the petition and of a copy thereof and of a copy of the court's order be made upon the parent by:

(2) Service by publication. If the residence of a parent is not known and cannot be ascertained, or if an attempt to effect service by either of the methods authorized in paragraph (1) is unsuccessful, the court may order that service shall be made by publication. The order shall direct that publication of notice of the pendency of the petition and of the time and place of the hearing thereof be made in a newspaper or newspapers suitable for the advertisement of notices of judicial proceedings once in each week for not less than four successive weeks as the court may prescribe, the last publication to be not less than twenty-one days prior to the time appointed for the hearing of the petition. The court, in addition to ordering publication, may direct that a copy of the petition and notice be forthwith deposited in the post office, addressed to the parent at the parent's last known place of residence. The service of the notice required by section 578-2 shall be deemed complete at the expiration of the time prescribed by the order of publication.