LP and SDP branch-and-cut algorithms for the minimum graph bisection problem: a computational comparison

Orienteering Problem with Variable Profits, Fractional Objective Function and Demand on Arcs

Nowadays, due to the high expectations of customers in meeting their demand and the competition environment among service providers, employers are working to provide customers with new methods in the shortest possible time and in the best possible way to attract customer’s satisfaction and maximize profits. In this paper, the orienteering problem with variable profits, fractional objective func...

Approximation Algorithms for the Bipartite Multi-cut Problem

We introduce the Bipartite Multi-cut problem. This is a generalization of the st-Min-cut problem, is similar to the Multi-cut problem (except for more stringent requirements) and also turns out to be an immediate generalization of the Min UnCut problem. We prove that this problem is NP-hard and then present LP and SDP based approximation algorithms. While the LP algorithm is based on the Garg-V...

An Efficient Semidefinite Programming Relaxation for the Graph Partition Problem

We derive a new semidefinite programming relaxation for the general graph partition problem (GPP). Our relaxation is based on matrix lifting with matrix variable having order equal to the number of vertices of the graph. We show that this relaxation is equivalent to the Frieze-Jerrum relaxation [A. Frieze and M. Jerrum. Improved approximation algorithms for max k-cut and max bisection. Algorith...

A Comparative Study of Linear and Semidefinite Branch-and-Cut Methods for Solving the Minimum Graph Bisection Problem

On the Parameterized Complexity of Computing Graph Bisections

The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that Bisection is FPT w.r.t. the minimum c...