Fast algorithm for creating space efficient dispatching tables with application to multi-dispatching

TL;DR: This paper shows how to extend one such solution to the multiple-inheritance~(MI) setting, with an increase to the space requirement by a small factor of κ, which can be thought of as a metric of the complexity of the topology of the inheritance hierarchy.

Abstract: The dispatching problem can be solved very efficiently in the single-inheritance~(SI) setting. In this paper we show how to extend one such solution to the multiple-inheritance~(MI) setting. This generalization comes with an increase to the space requirement by a small factor of κ This factor can be thought of as a metric of the complexity of the topology of the inheritance hierarchy.On a data set of~35 hierarchies totaling some~64 thousand types, our dispatching data structure, based on a novel type slicing technique, exhibits very significant improvements over previous dispatching techniques, not only in terms of the time for creating the underlying data structure, but also in terms of total space used.The cost is in the dispatching time, which is no longer constant, but doubly logarithmic in the number of types. Conversely, by using a simple binary search, dispatching time is logarithmic in the number of different implementations. In practice dispatching uses one indirect branch and, on average, only~2.5 binary branches.Our results also have applications to the space-efficient implementation of the more general problem of dispatching multi-methods.A by-product of our type slicing technique is an incremental algorithm for constant-time subtyping tests with favorable memory requirements. (The incremental version of the subtyping problem is to maintain the subtyping data structure in presence of additions of types to the inheritance hierarchy.)