# Inapproximability of the Max-cut Problem with Negative Weights

• Hong, Sung-Pil (Department of Industrial Engineering, Seoul National University)
• Published : 2008.05.31

#### Abstract

We show that when a max-cut problem is allowed native-weight edges, to decide if the problem has a cut of a positive weight is NP-hard. This implies that there is no polynomial time algorithm which guarantees a cut whose objective value is no less than $1/p(<I>)$ times the optimum for any polynomially computable polynomial p, where denotes the encoding length of an instance I.

#### References

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