On reduction integer programs to knapsack problem

TL;DR

This paper proposes a new method to reduce general integer programming problems to the knapsack problem, potentially simplifying their solution process.

Contribution

It introduces a novel reduction technique transforming integer programs into knapsack problems, facilitating easier solving strategies.

Findings

The reduction method is applicable to a broad class of integer programs.

It preserves the optimal solutions during the reduction.

Potential for improved solution algorithms for integer programming.

Abstract

Let $A$ be an integral nonnegative $m\times n$ matrix, $b$ be an integral nonnegative vector. It is suggested new method for reduction of integer program $\max \{cx| Ax=b, x\ge 0, x\in\mathbf{Z}^n\}$ to knapsack problem $\max \{c'x| fAx=fb, x\ge 0, x\in\mathbf{Z}^n\}$.