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We consider the following scheduling problem. There are m parallel machines and n independent jobs. Each job is to be assigned to one of the machines. The processing of job j on machine i requires time pij. The objective is to find a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum...
We present a preprocessing algorithm to make certain polynomial algorithms strongly polynomial. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective function w. Our preprocessing algorithm replaces w by an integral valued w whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal...
A network is a graph with numeric parameters such as edge lengths, capacities, costs, etc. We present efficient algorithms for network problems that work by scaling the numeric parameters. Scaling takes advantage of efficient nonnumeric algorithms such as the Hopcroft-Karp matching algorithm. Let n, m and N denote the number of vertices, number of edges, and largest numeric parameter of the network,...
Fully polynomial approximation algorithms for knapsack problems are presented. These algorithms are based on ideas of Ibarra and Kim, with modifications which yield better time and space bounds, and also tend to improve the practicality of the procedures. Among the principal improvements are the introduction of a more efficient method of scaling and the use of a median-finding routine to eliminate...
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