Are references bi-directional, in the sense that given ?cat, datomic does no searching to find the related entity, ?person, in a [?person :pet ?cat] restriction?
Or should I manually build a reference in the other side (e.g. setting an :owner attribute for pets) to prevent a linear search in all the ?persons that have :pets?
No, There is no speed advantage to storing both sides of a relation explicitly, all relations are bi-directional in datomic.