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.
@article{arxiv.2108.02290,
title = {Relational E-Matching},
author = {Yihong Zhang and Yisu Remy Wang and Max Willsey and Zachary Tatlock},
journal= {arXiv preprint arXiv:2108.02290},
year = {2022}
}