Specifically, the linked paper models indexes on a table as sets of n-dimensional volumes showing where rows aren&#x27;t. It then gives a join algorithm that is asymptotically instance-optimal (up to a poly-log factor) ie better than any previous result.<p>Unfortunately it relies on efficiently representing and querying the set of volumes built up during the query process and the data structure used in the paper is ridiculously impractical. I haven&#x27;t seen an implementation yet that managed to tame the constant factors. Perhaps seeing how the OP models volumes&#x2F;constraints would help.