Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time

Radoslaw Hofman

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Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time

Radoslaw Hofman

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Abstract

This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial time, what places them in P class. During past three years there appeared some articles using LP to solve NP-complete problems. This methods use large number of variables (O(n^9)) solving correctly almost all instances that can be solved in reasonable time. Can they solve infinitively large instances? This article gives answer to this question.

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BibTeX RIS

Radoslaw Hofman. 2006-11-02. Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time. https://arxiv.org/abs/cs/0611008

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