(Really) Tight bounds for dispatching binary methods

TL;DR

This paper presents a new method for binary dispatching in object-oriented programming that achieves logarithmic query time with linear preprocessing, improving over previous solutions that required superlinear construction time.

Contribution

It introduces a linear-time, linear-space data structure for binary dispatching with logarithmic query time, and further refines query time to slightly sublogarithmic, matching known lower bounds.

Findings

Linear-time construction of dispatching structure

Logarithmic query time achieved

Sublogarithmic query time optimized

Abstract

We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the run-time we are able to retrieve the most specialized implementation which can be invoked with the actual types of the arguments. For the binary dispatching, where the methods take exactly two arguments, logarithmic query time is possible, even if the structure is allowed to take linear space. Unfortunately, known solutions achieving such complexity require superlinear time for constructing the structure. Using a different idea we are able to construct in (deterministic) linear time and space a structure allowing dispatching binary methods in the same logarithmic time. Then we show how to improve the query time to slightly sublogarithmic, which is easily seen to be optimal as a consequence of some already known lower bounds if we want to keep the size of the resulting structure close to linear.