There is an issue of A/B plane partition of HSTPs in the topology optimization of CCS7 network. It can be formulated into a new kind of graph partition problem.

The hypergraph denoting circuit is transformed into a weighted undirected graph, so the problem of circuit bisection is transformed into the graph partition problem.

Since the graph partition problem has the well known SDP (semidefinite programming) relaxation, the strengthened SDP relaxation is achieved by an addition of two nonlinear constraints to SDP relaxation. Theory and numerical experiment ensure that the strengthened SDP relaxation gives the problem of circuit bisection a lower bound greater than exited lower bownds.

There is an issue of A/B plane partition of HSTPs in the topology optimization of CCS7 network. It can be formulated into a new kind of graph partition problem.

The hypergraph denoting circuit is transformed into a weighted undirected graph, so the problem of circuit bisection is transformed into the graph partition problem.

Since the graph partition problem has the well known SDP (semidefinite programming) relaxation, the strengthened SDP relaxation is achieved by an addition of two nonlinear constraints to SDP relaxation. Theory and numerical experiment ensure that the strengthened SDP relaxation gives the problem of circuit bisection a lower bound greater than exited lower bownds.

A linear integer-programming algorithm has been implemented to solve the graph partition problem rigorously and efficiently.

We have formulated the problem as a graph partition problem.

We show how this technique can be applied to the Quadratic Assignment Problem, the Graph Partition Problem and the Max-Clique Problem.

This result on extended neighborhoods relies on a proof that the convex hull of solutions for the graph partition problem has a diameter of 1, that is, every two corner points of this polytope are adjacent.

We also show that the extended neighborhood for the graph partition problem is the same as the original neighborhood, regardless of the neighborhood defined.

This paper shows a graph partition problem pblynomially solvable. Moreover, the problemin the planar case leads to a number of problems in graphs and combinatorial optimisationspolynomially solvable.

There is an issue of A/B plane partition of HSTPs in the topology optimization of CCS7 network. It can be formulated into a new kind of graph partition problem. The problem is proved to be NP-complete, so the neural network, the genetic algorithm and the simulated annealing are applied to solve it. In order to make the algorithms comparable, the testing schemes are carefully designed. The computing results for the three algorithms show that the genetic algorithm and the simulated annealing are quite...

There is an issue of A/B plane partition of HSTPs in the topology optimization of CCS7 network. It can be formulated into a new kind of graph partition problem. The problem is proved to be NP-complete, so the neural network, the genetic algorithm and the simulated annealing are applied to solve it. In order to make the algorithms comparable, the testing schemes are carefully designed. The computing results for the three algorithms show that the genetic algorithm and the simulated annealing are quite robust for the problem, they can search out the optimum with a larger probability and a higher efficiency.

The hypergraph denoting circuit is transformed into a weighted undirected graph, so the problem of circuit bisection is transformed into the graph partition problem. Since the graph partition problem has the well known SDP (semidefinite programming) relaxation, the strengthened SDP relaxation is achieved by an addition of two nonlinear constraints to SDP relaxation. Theory and numerical experiment ensure that the strengthened SDP relaxation gives the problem of circuit bisection a lower bound...

The hypergraph denoting circuit is transformed into a weighted undirected graph, so the problem of circuit bisection is transformed into the graph partition problem. Since the graph partition problem has the well known SDP (semidefinite programming) relaxation, the strengthened SDP relaxation is achieved by an addition of two nonlinear constraints to SDP relaxation. Theory and numerical experiment ensure that the strengthened SDP relaxation gives the problem of circuit bisection a lower bound greater than exited lower bownds.