This paper concerns the solution of the NP-hard max-bisection problems. NCP functions are employed to convert max-bisection problems into continuous nonlinear programming problems. Solving the resulting continuous non...This paper concerns the solution of the NP-hard max-bisection problems. NCP functions are employed to convert max-bisection problems into continuous nonlinear programming problems. Solving the resulting continuous nonlinear programming problem generates a solution that gives an upper bound on the optimal value of the max-bisection problem. From the solution, the greedy strategy is used to generate a satisfactory approximate solution of the max-bisection problem. A feasible direction method without line searches is proposed to solve the resulting continuous nonlinear programming, and the convergence of the algorithm to KKT point of the resulting problem is proved. Numerical experiments and comparisons on well-known test problems, and on randomly generated test problems show that the proposed method is robust, and very efficient.展开更多
Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of cro...Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.展开更多
文摘This paper concerns the solution of the NP-hard max-bisection problems. NCP functions are employed to convert max-bisection problems into continuous nonlinear programming problems. Solving the resulting continuous nonlinear programming problem generates a solution that gives an upper bound on the optimal value of the max-bisection problem. From the solution, the greedy strategy is used to generate a satisfactory approximate solution of the max-bisection problem. A feasible direction method without line searches is proposed to solve the resulting continuous nonlinear programming, and the convergence of the algorithm to KKT point of the resulting problem is proved. Numerical experiments and comparisons on well-known test problems, and on randomly generated test problems show that the proposed method is robust, and very efficient.
基金Research partly supported by Chinese NSF grant 19731001 and National 973 Information Technology and High-Performance Software Program of China with grant No.G1998030401.The first author gratefully acknowledges the support of K.C.Wong Education Foundat
文摘Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.
