Near Optimal Hierarchical Encoding of Types

A type inclusion test is a procedure to decide whether two types are related by a given subtyping relationship. An e cient implementation of the type inclusion test plays an important role in the performance of object oriented programming languages with multiple subtyping like C++, Ei el or Java. There are well-known methods for performing fast constant time type inclusion tests that use a hierarchical bit vector encoding of the partial ordered set representing the type hierarchy. The number of instructions required by the type inclusion test is proportional to the length of those bit vectors. We present a new algorithm based on graph coloring which computes a near optimal hierarchical encoding of type hierarchies. The new algorithm improves signi cantly on previous results { it is faster, simpler and generates smaller bit vectors.