A max-cut formulation of 0/1 programs

TL;DR

This paper demonstrates that 0/1 integer programming problems can be reformulated as MAX-CUT problems, enabling the use of MAX-CUT approximation techniques and comparing various relaxation bounds.

Contribution

It introduces a novel MAX-CUT formulation for 0/1 programs, linking them to graph-based approaches and relaxation bounds.

Findings

MAX-CUT formulation applies to linear and quadratic 0/1 programs

Semidefinite relaxation bounds are compared with LP and other relaxations

The approach broadens the toolkit for solving 0/1 integer programs

Abstract

We show that the linear or quadratic 0/1 program\[P:\quad\min\{ c^Tx+x^TFx : \:A\,x =b;\:x\in\{0,1\}^n\},\]can be formulated as a MAX-CUT problem whose associated graph is simply related to the matrices $\F$ and $\A^T\A$.Hence the whole arsenal of approximation techniques for MAX-CUT can be applied. We also compare the lower boundof the resulting semidefinite (or Shor) relaxation with that of the standard LP-relaxation and the first semidefinite relaxationsassociated with the Lasserre hierarchy and the copositive formulations of $P$.