The competitiveness of on-line assignments
Journal of Algorithms
Better Bounds for Online Scheduling
SIAM Journal on Computing
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
On-line algorithms for the channel assignment problem in cellular networks
Discrete Applied Mathematics
Online parallel machines scheduling with two hierarchies
Theoretical Computer Science
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
New lower and upper bounds for on-line scheduling
Operations Research Letters
| Hi-index | 5.23 |
This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize the makespan, i.e., the maximum load of all machines. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both the algorithm and the lower bound are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m=4 and 5, respectively.