A Reply to Hofman On: "Why LP cannot solve large instances of NP-complete problems in polynomial time"

Abstract

Using an approach that seems to be patterned after that of Yannakakis, Hofman argues that an NP-complete problem cannot be formulated as a polynomial bounded-sized linear programming problem. He then goes on to propose a "construct" that he claims to be a counter-example to recently published linear programming formulations of the Traveling Salesman Problem (TSP) and the Quadratic Assignment Problems (QAP), respectively. In this paper, we show that Hofman's construct is flawed, and provide further proof that his "counter-example" is invalid.