In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Ma...In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.展开更多
In this paper, we consider a uniform machine scheduling problem with nonsimultaneous available times. We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3). We tighten this bound when the machi...In this paper, we consider a uniform machine scheduling problem with nonsimultaneous available times. We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3). We tighten this bound when the machine speed ratio is small or m=2. Furthermore, we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.展开更多
基金Project (No. Y605316) supported by the Natural Science Foundationof Zhejiang Province, China and the Natural Science Foundation of the Education Department of Zhejiang Province (No. 20060578), China
文摘In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.
基金the National 973 Fundamental Research Project of Chinathe National Natural Sciences Foundation of China!19701028
文摘In this paper, we consider a uniform machine scheduling problem with nonsimultaneous available times. We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3). We tighten this bound when the machine speed ratio is small or m=2. Furthermore, we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.
