Persistency of linear programming relaxations for the stable set problem

Ellipsoidal Relaxations of the Stable Set Problem: Theory and Algorithms

A new exact approach to the stable set problem is presented, which attempts to avoid the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovász theta number. This ellipsoid can then be used to ...

Stronger Linear Programming Relaxations

A Semidefinite Programming Relaxation for the Generalized Stable Set Problem

In this paper, we generalize the theory of a convex set relaxation for the maximum weight stable set problem due to Grotschel, Lov asz and Schrijver to the generalized stable set problem. We de ne a convex set which serves as a relaxation problem, and show that optimizing a linear function over the set can be done in polynomial time. This implies that the generalized stable set problem for per...

Linear programming relaxations of maxcut

It is well-known that the integrality gap of the usual linear programming relaxation for Maxcut is 2 − ǫ. For general graphs, we prove that for any ǫ and any fixed boundk, adding linear constraints of support bounded by k does not reduce the gap below 2−ǫ. We generalize this to prove that for any ǫ and any fixed bound k, strengthening the usual linear programming relaxation by doing k rounds of...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.