Compact Binary Relation Representations with Rich Functionality

TL;DR

This paper introduces new compact binary relation data structures that support a wide range of queries efficiently, addressing limitations of previous specialized representations.

Contribution

It generalizes binary relation operations, identifies their interrelations, and proposes novel, space-efficient data structures supporting many useful queries.

Findings

New binary relation representations support numerous queries efficiently.

Proposed structures are space-efficient and versatile.

The approach unifies and extends previous methods.

Abstract

Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify many of those operations arising in applications and generalize them into a wide set of desirable queries for a binary relation representation. We also identify reductions among those operations. We then introduce several novel binary relation representations, some simple and some quite sophisticated, that not only are space-efficient but also efficiently support a large subset of the desired queries.