Height counting of unlabeled interval and N-free posets

AbstractThis paper enumerates according to height the classes of unlabeled N-free posets, interval orders, and posets that are both N-free and interval orders. The last two classes are enumerated according to height in terms of generating functions. We apply an algorithmic method for height counting of connected N-free posets. Numerical results for n-element posets of height k, 1⩽k⩽n⩽14, are included

Sort-Mid tasks scheduling algorithm in grid computing

Scheduling tasks on heterogeneous resources distributed over a grid computing system is an NP-complete problem. The main aim for several researchers is to develop variant scheduling algorithms for achieving optimality, and they have shown a good performance for tasks scheduling regarding resources selection. However, using of the full power of resources is still a challenge. In this paper, a new heuristic algorithm called Sort-Mid is proposed. It aims to maximizing the utilization and minimizing the makespan. The new strategy of Sort-Mid algorithm is to find appropriate resources. The base step is to get the average value via sorting list of completion time of each task. Then, the maximum average is obtained. Finally, the task has the maximum average is allocated to the machine that has the minimum completion time. The allocated task is deleted and then, these steps are repeated until all tasks are allocated. Experimental tests show that the proposed algorithm outperforms almost other algorithms in terms of resources utilization and makespan