Minimum-move traversal of completely mobile resolving sets

Determine the smallest number of legal resolving moves required for every robot in a given completely mobile resolving set to visit every vertex of the graph, and develop algorithms that optimize such traversal sequences by move count.

Background

Completely mobile resolving sets require every robot to traverse every vertex while the occupied vertices remain a resolving set after each legal move. The paper establishes existence and metric-dimension results for several graph classes, but does not analyze the efficiency of the resulting traversal sequences.

The unresolved problem is to optimize traversal length for a fixed completely mobile resolving set. This introduces an algorithmic optimization question concerning the number of legal moves needed to achieve full traversal by all robots.