Efficient subtyping tests with PQ-encoding

Given a type hierarchy, a subtyping test determines whether one type is a direct or indirect descendant of another type. Such tests are a frequent operation during the execution of object-oriented programs. The implementation challenge is in a space-efficient encoding of the type hierarchy that simultaneously permits efficient subtyping tests. We present a new scheme for encoding multiple- and single-inheritance hierarchies, which, in the standard benchmark hierarchies, reduces the footprint of all previously published schemes. Our scheme is called PQ-encoding (PQE) after PQ-trees , a data structure previously used in graph theory for finding the orderings that satisfy a collection of constraints. In particular, we show that in the traditional object layout model, the extra memory requirements for single-inheritance hierarchies is zero. In the PQE subtyping, tests are constant time, and use only two comparisons. The encoding creation time of PQE also compares favorably with previous results. It is less than 1 s on all standard benchmarks on a contemporary architecture, while the average time for processing a type is less than 1 ms. However, PQE is not an incremental algorithm. Other than PQ-trees, PQE employs several novel optimization techniques. These techniques are applicable also in improving the performance of other, previously published, encoding schemes.