TY - GEN
T1 - Online scheduling of jobs with fixed start times on related machines
AU - Epstein, Leah
AU - Jez, Łukasz
AU - Sgall, Jiří
AU - Van Stee, Rob
PY - 2012
Y1 - 2012
N2 - We consider online preemptive scheduling of jobs with fixed starting times revealed at those times on m uniformly related machines, with the goal of maximizing the total weight of completed jobs. Every job has a size and a weight associated with it. A newly released job must be either assigned to start running immediately on a machine or otherwise it is dropped. It is also possible to drop an already scheduled job, but only completed jobs contribute their weights to the profit of the algorithm. In the most general setting, no algorithm has bounded competitive ratio, and we consider a number of standard variants. We give a full classification of the variants into cases which admit constant competitive ratio (weighted and unweighted unit jobs, and C-benevolent instances, which is a wide class of instances containing proportional-weight jobs), and cases which admit only a linear competitive ratio (unweighted jobs and D-benevolent instances). In particular, we give a lower bound of m on the competitive ratio for scheduling unit weight jobs with varying sizes, which is tight. For unit size and weight we show that a natural greedy algorithm is 4/3-competitive and optimal on m = 2 machines, while for a large m, its competitive ratio is between 1.56 and 2. Furthermore, no algorithm is better than 1.5-competitive.
AB - We consider online preemptive scheduling of jobs with fixed starting times revealed at those times on m uniformly related machines, with the goal of maximizing the total weight of completed jobs. Every job has a size and a weight associated with it. A newly released job must be either assigned to start running immediately on a machine or otherwise it is dropped. It is also possible to drop an already scheduled job, but only completed jobs contribute their weights to the profit of the algorithm. In the most general setting, no algorithm has bounded competitive ratio, and we consider a number of standard variants. We give a full classification of the variants into cases which admit constant competitive ratio (weighted and unweighted unit jobs, and C-benevolent instances, which is a wide class of instances containing proportional-weight jobs), and cases which admit only a linear competitive ratio (unweighted jobs and D-benevolent instances). In particular, we give a lower bound of m on the competitive ratio for scheduling unit weight jobs with varying sizes, which is tight. For unit size and weight we show that a natural greedy algorithm is 4/3-competitive and optimal on m = 2 machines, while for a large m, its competitive ratio is between 1.56 and 2. Furthermore, no algorithm is better than 1.5-competitive.
UR - http://www.scopus.com/inward/record.url?scp=84865293353&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-32512-0_12
DO - 10.1007/978-3-642-32512-0_12
M3 - Conference contribution
AN - SCOPUS:84865293353
SN - 9783642325113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 134
EP - 145
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
Y2 - 15 August 2012 through 17 August 2012
ER -