In this paper, we consider a class of quadratic maximization problems. For a subclass of the problems, we show that the SDP relaxation approach yields an approximation solution with the worst-case performance ratio at least α = 0.87856 ⋯. In fact, the estimated worst-case performance ratio is dependent on the data of the problem with α being a uniform lower bound. In light of this new bound, we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α + δ d if every weight is strictly positive, where δ d > 0 is a constant depending on the problem dimension and data.
Bibliographical noteFunding Information:
Received April 4, 2006; accepted March 14, 2007; published online July 31, 2007 DOI: 10.1007/s11425-007-0080-x † Corresponding author This work was supported by the National Natural Science Foundation of China (Grant No. 10401038) and Startup Grant for Doctoral Research of Beijing University of Technology and Hong Kong RGC Earmarked Grant CUHK4242/04E
- Approximation algorithm
- Max-cut problem
- Performance ratio
- Quadratic maximization
- Semidefinite programming relaxation