On Quadratization of Pseudo-Boolean Functions

TL;DR

This paper surveys existing methods for transforming high-degree pseudo-Boolean functions into quadratic form and introduces new techniques, including multiple splits and an aggregative approach based on common parts.

Contribution

It presents novel quadratization methods, including a new splitting technique and the first aggregative approach for pseudo-Boolean functions.

Findings

Introduces a new multiple splitting technique for quadratization.

Proposes the first aggregative approach based on common parts.

Provides a comprehensive survey of current quadratization methods.

Abstract

We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of terms based on their common parts.