Relational E-Matching

POPL 2022, January 2022
  title={Relational E-Matching}, 
    Yihong Zhang and 
    Yisu Remy Wang and 
    Max Willsey and 
    Zachary Tatlock


We present a new approach to e-matching based on relational join; in particular, we apply recent database query execution techniques to guarantee worst-case optimal run time. Compared to the conventional backtracking approach that always searches the e-graph “top down”, our new relational e-matching approach can better exploit pattern structure by searching the e-graph according to an optimized query plan. We also establish the first data complexity result for e-matching, bounding run time as a function of the e-graph size and output size. We prototyped and evaluated our technique in the state-of-the-art egg e-graph framework. Compared to a conventional baseline, relational e-matching is simpler to implement and orders of magnitude faster in practice.

By reducing e-matching queries conjunctive queries, we achieve practical and theoretical speedup. This slide comes from Yihong's PLDI 2021 SRC poster that won 1st place.