Optimal online algorithms on two hierarchical machines with tightly-grouped processing times

Semi-online scheduling: A survey

“…Machines are available on demand and the release time (r j ) of machine M j is known in advance [64]. Some authors have also considered the scenario where one machine is available for all jobs and other machine is available for few designated jobs [82]. -Grade of Service (GOS) or Machine Hierarchy.…”

Online scheduling on parallel machines: A survey

“…林凌等: 平行机在线排序综述 [45] , P 2|UB&LB|Cmax [46] 与 P 2|g = 2, sum, UB&LB|Cmax [47,48] (两问题竞争比相同), P 2|decr, UB&LB|Cmax [49] ; 虚线: 自上至下, P 2|g = 2, UB&LB|C min [50] , P 2|UB&LB|C min [51] 与 P 2|g = 2, sum, UB&LB|C min [50] (两问题竞争比相同)); (c) 两 台有等级同类机在线与半在线问题最好算法竞争比 (实线: 自上至下, Q2|g = 2|Cmax [52] , Q2|g = 2, pmpt|Cmax (参见文献 [53]), Q2|g = 2, frac|Cmax [54] ; 虚线: 自上至下, Q2|g = 2, max |Cmax [55] , Q2|g = 2, opt|Cmax 与 Q2|g = 2, sum|Cmax [55] (两问题竞争比相同)); (d) 两台同类机可拒绝在线与半在线问题下界与算法竞争比 (实线: 在线问题最佳参数下界与最佳算法参数竞争比 [56,57] ; 虚线: 自上至下, 可中断 [56] , 单位工件且可中断 [58] , 单位工件并按罚值非增顺序到达且可中断 [58] 三问题最好算法竞争比) [63,64] . Englert 等 [64]…”

Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing

“…Liu et al (2011) studied the problem with bounded jobs, i.e., the processing time of each job is bounded with in an interval [a, αa] with α ≥ 1 on two machines. Recently, Zhang et al (2015) provided a best possible online algorithm for the problem. Chen et al (2013) considered two semi-online hierarchical scheduling with the buffer or rearrangement on two identical machines to minimize the makespan.…”