Strengthened semidefinite relaxations via a second lifting for the Max-Cut problem
نویسندگان
چکیده
منابع مشابه
Strengthened Semidefinite Programming Relaxations for the Max-cut Problem
In this paper we summarize recent results on finding tight semidefinite programming relaxations for the Max-Cut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of Max-Cut and in particular we make no assumptions on the edge weights. We present two strengthenings of the well-known semidefinite programming relaxation of Max-Cut studied by Goemans and...
متن کاملA Tight Semidefinite Relaxation of the MAX CUT Problem
We obtain a tight semidefinite relaxation of the MAX CUT problem which improves several previous SDP relaxation in the literature. Not only is it a strict improvement over the SDP relaxation obtained by adding all the triangle inequalities to the well-known SDP relaxation, but also it satisfy Slater constraint qualification (strict feasibility).
متن کاملSemideenite Relaxations for Max-cut
We compare several semideenite relaxations for the cut polytope obtained by applying the lift and project methods of Lovv asz and Schrijver and of Lasserre. We show that the tightest relaxation is obtained when aplying the Lasserre construction to the node formulation of the max-cut problem. This relaxation Q t (G) can be deened as the projection on the edge subspace of the set F t (n), which c...
متن کاملApproximation Bounds for Max-Cut Problem with Semidefinite Programming Relaxation
In this paper, we consider the max-cut problem as studied by Goemans and Williamson [8]. Since the problem is NP-hard in general, following Goemans and Williamson, we apply the approximation method based on the semidefinite programming (SDP) relaxation. 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 thi...
متن کاملA Branch and Bound Algorithm for Max-Cut Based on Combining Semidefinite and Polyhedral Relaxations
In this paper we present a method for finding exact solutions of the Max-Cut problem maxxLx such that x ∈ {±1}. We use a semidefinite relaxation combined with triangle inequalities, which we solve with the bundle method. This approach is due to Fischer, Gruber, Rendl, and Sotirov [12] and uses Lagrangian duality to get upper bounds with reasonable computational effort. The expensive part of our...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2002
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(01)00266-9