  The results of a comprehensive and systematic ab-initio based ground-state
search for the structural arrangement of oxygen vacancies in rutile phase
TiO$_2$ provide new insights into their memristive properties. We find that O
vacancies tend to form planar arrangements which relax into structures
exhibiting metallic behavior. These meta-stable arrangements are structurally
akin to, yet distinguishable from the Magn\'eli phase. They exhibit a more
pronounced metallic nature, but are energetically less favorable. Our results
confirm a clear structure-property relationship between segregated oxygen
vacancy arrangement and metallic behavior in reduced oxides.
