Improved Analysis of a Max-Cut Algorithm Based on Spectral Partitioning

Improved Analysis of a Max Cut Algorithm Based on Spectral Partitioning

Luca Trevisan [1] presented an approximation algorithm for Max Cut based on spectral partitioning techniques. He proved that the algorithm has an approximation ratio of at least 0.531. We improve this bound up to 0.6142. We also define and extend this result for the more general Maximum Colored Cut problem.

A Continuation Algorithm for Max-Cut Problem

A continuation algorithm for the solution of max-cut problems is proposed in this paper. Unlike the available semi-definite relaxation, a max-cut problem is converted into a continuous nonlinear programming by employing NCP functions, and the resulting nonlinear programming problem is then solved by using the augmented Lagrange penalty function method. The convergence property of the proposed a...

Improved approximation of Max-Cut on graphs of bounded degree

We analyze the addition of a simple local improvement step to various known ran-domized approximation algorithms. Let ' 0:87856 denote the best approximation ratio currently known for the Max Cut problem on general graphs GW95]. We consider a semideenite relaxation of the Max Cut problem, round it using the random hyperplane rounding technique of ((GW95]), and then add a local improvement step....

A Min-max Cut Algorithm for Graph Partitioning and Data Clustering

Branch and Cut based on the volume algorithm: Steiner trees in graphs and Max-cut

Abstract. We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cu...