In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain t...In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.展开更多
This article reports a case of thoracic aortic aneurysm with hemoptysis as the first clinical manifestation, hemoptysis as the first clinical manifestation is very uncommon and to the best of our knowledge, only twent...This article reports a case of thoracic aortic aneurysm with hemoptysis as the first clinical manifestation, hemoptysis as the first clinical manifestation is very uncommon and to the best of our knowledge, only twenty of such cases have been previously reported. The case report presented here constitutes the longest course of the disease reported in medical literature, and good recovery after thoracic endovascular aortic repair, may help us to increase the understanding and diagnosis of the disease.展开更多
基金Supported by the National Natural Science Foundation of China(11001242,11071220)
文摘In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.
文摘This article reports a case of thoracic aortic aneurysm with hemoptysis as the first clinical manifestation, hemoptysis as the first clinical manifestation is very uncommon and to the best of our knowledge, only twenty of such cases have been previously reported. The case report presented here constitutes the longest course of the disease reported in medical literature, and good recovery after thoracic endovascular aortic repair, may help us to increase the understanding and diagnosis of the disease.
