The relabel-to-front push-relabel algorithm<ref name="clrs26"/> organizes all vertices into a linked list.Initially,and maintains the nodesinvariant canthat bethe insertedlist inis [[Topological sorting|topologically sorted]] with respect to the arbitraryadmissible ordernetwork. The algorithm scans the list from front to back and performs a discharge operation on the current vertex if it is active. If the node is relabeled, it is moved to the front of the list, and the scan is restarted from the front.
The algorithm also has {{nowrap|''O''(''V''<sup>3</sup>)}} time complexity.
