Haeder Younis Ghawi

In this paper, we give some basic notions concerning the st-connected vertex separator problem(st-CVS problem), then we give mathematical formula for st-CVS problem, then some special cases on some types of graphs , after then introduce an integer programming formulations for this problem. Also, we introduce a heuristic to solve this problem.

In this paper, we propose a practical and efficient methods to solve the vertex separator problem (VSP for short), based on branch-and-bound procedure, which uses linear programming, and a greedy algorithm. This problem arises in many areas of applications such as graph algorithms, communication networks, solving systems of equations, finite element and finite difference problems. We show, by computational experiments, that our approach is able to solve in short time large-scale instances of VSP from the literature to optimality or near optimality.

In the present paper, we have introduced a subclass S(γ, α, µ) of univalent functions with negative coefficients in the unit disc. We derive basic properties like coefficient inequality, distortion and covering theorem, radius of convexity, extreme points, Hadamard product, closure theorems and convolution operator for functions belonging to this class.

n the problem of scheduling a single machine to minimize the sum of completion time and total late work, there are n jobs to be processed for which each has an integer processing time and a due date. The objective is to minimize the sum of total completion time and total late work ,where the late work for a job is the amount of processing of this job that is performed after its due date. Although dominance rules are derived for the special cases in which all processing times are equal and all due dates are equal. Algorithm H is presented for the general non preemptive sum of completion time and the total late work simultaneous problems

In this paper, to minimize a function of three cost criteria for scheduling n jobs on a single machine , the problem is discussed : {Minimizing a function of three criteria maximum tardiness ,maximum earliness and sum square of completion time in hierarchical method }.

In this study, to minimize a function of two cost criteria for scheduling n jobs on a single machine , the problem is discussed : “ Minimizing a function of total square completion time and maximum Earliness simultaneously”. For this problem we proposed some algorithms to find exact(optimal) solution for hierarchical case and efficient (pareto optimal) solutions for simultaneous case. Also we proposed branch and bound algorithm to find exact solution for sum of total square completion time and maximum Earliness ,and present algorithm D to find exact solution in a fast way with respect to (BAB) method. We present computational experience for the (BAB) method and algorithm(D) on a large set of test problems

In this study, to minimize a function of two cost criteria for scheduling n jobs on a single machine , the problem is discussed : “ Minimizing a function of total square completion time and maximum Earliness simultaneously”. For this problem we proposed some algorithms to find exact(optimal) solution for hierarchical case and efficient (pareto optimal) solutions for simultaneous case. Also we proposed branch and bound algorithm to find exact solution for sum of total square completion time and maximum Earliness ,and present algorithm D to find exact solution in a fast way with respect to (BAB) method. We present computational experience for the (BAB) method and algorithm(D) on a large set of test problems