We examine the problem of scheduling n jobs, each of which must be processed by m machines. If the order in which a given job is processed on the machines is not fixed, the system is called an open shop. This situation might occur in testing components of an electronic system or doing repair work on an automobile. The computational difficulty of solving most open shop problems is known, with the majority being NP-hard. The computational difficulty of a few special cases is unknown, most notably when the jobs have identical processing time and the measure of performance is a function of job due dates. We reduce this uncertainty by developing polynomial algorithms to minimize the total tardiness and the number of tardy jobs in an open shop with identical processing time jobs.
Most recently, multicast communication has been included in multicomputer systems. Multicast communication refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. The performance of multicomputers is highly dependent on the message routing scheme and the communication mechanism. Wormhole routing is the most promising switching technique used in the new generation multicomputers. In this paper, we propose a multicast wormhole routing algorithm for 2D-torus multicomputers. The multicast routing algorithm is based on a path-like routing scheme and offers deadlock-free routing. Our simulation which compared the 2D-mesh multicomputers shows that the multipath routing algorithm for 2D-torus multicomputers can reduce the communication traffic and the maximum distance in multicast communication.
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