Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

Inapproximability of the Max-cut Problem with Negative Weights

  • Hong, Sung-Pil (Department of Industrial Engineering, Seoul National University)
  • Published : 2008.05.31
Download PDF
⟨ Previous Next ⟩

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.

Keywords

References

  1. Goemans, M. X. and D. P. Williamson, "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming," J. ACM 42 (1995) 1115-1145 https://doi.org/10.1145/227683.227684
  2. Matula, D. W. and F. Shahrokhi, Sparsest cuts and bottleneck in graphs, Discrete Appl. Math., 27 (1990) 113-123 https://doi.org/10.1016/0166-218X(90)90133-W
  3. McCormick, S. T., M. R. Rao, and G. Rinaldi, Easy and difficult objective functions for max cut, Math. Program, Ser. B 94 (2003) 459-466 https://doi.org/10.1007/s10107-002-0328-8
  4. Vazirani, V. V., Approximation algorithms, Springer, Berlin, 2001