Monday, April 23, 2018

Addendum to the MILP Optimization Times

In our upcoming SIGMOD paper on Adaptive Optimization of Very Large Join Queries we compared result quality and optimization times of over a dozen approaches for join ordering, over a wide range of query sizes. Which is quite a challenging problem, as the different algorithms often work under different assumptions, usually no reference implementation is available, and we had to unify them all into one framework that can handle joins from 10 to 5,000 relations.

One of the approaches that we included was Solving the Join Ordering Problem via Mixed Integer Linear Programming by and Christoph Koch. Our implementation tries to follow the original paper faithfully, implementing the mapping from query graph to MILP problem just as described in the original paper. For some benchmarks like TPC-DS (up to 18 relations in a join, with a median of 3) that implementation worked fine. But for some other benchmarks like the Join Order Benchmark (up to 17 relations, median 8) and the SQLite join set (up to 64 relations, median 34) we saw significant optimization times on our Xeon E7-4870 system: In total 290s for the JOB queries, and 5,100s for the SQLite queries. (Note that the JOB times do not include queries with non-inner join edges, as these currently cannot be handled by the MILP approach).

Immanuel pointed out to me that we can improve the optimization time quite a bit by initializing the start position for the Gurobi solver to a solution constructed by a greedy heuristic. In particular for the SQLite queries that helps a lot, as the greedy solution works very well there and thus the start position is already very good. The optimization times for his implementation (on a weaker hardware, a 2.2 GHz Intel Core i7 laptop) are 52s for the Join Order Benchmark and 44s for the SQLite queries.

I am glad for the hint, and thus amend the numbers here. As far as a I can see it this initialization trick was not mentioned in the original SIGMOD17 paper. But of course a carefully tuned implementation will often have tricks that are unfortunately not described in detail in the corresponding publication.

If there are any more comments about any of the approaches we measured I am happy to hear them.

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