Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Dynamic scheduling on parallel machines
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Scheduling Parallel Machines On-line
SIAM Journal on Computing
Competitive analysis of network load balancing
Journal of Parallel and Distributed Computing
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Competitive implementation of parallel programs
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On-line scheduling of parallel jobs with runtime restrictions
Theoretical Computer Science
Developments from a June 1996 seminar on Online algorithms: the state of the art
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
| Hi-index | 5.23 |
We study an on-line problem of scheduling parallel jobs on two-dimensional meshes. Parallel jobs arrive dynamically according to the dependencies between them, which are unknown before the jobs appear. Each job may need more than one processor simultaneously and is required to be scheduled on a submesh of the processors which are located on a two-dimensional mesh, i.e., a job must be scheduled on a rectangle of given dimensions. The objective is to minimize the maximum completion time (makespan). We deal with a UET job system, in which all job processing times are equal. We show a lower bound of 3.859 and present a 5.25-competitive algorithm. It significantly improves a previous lower bound of 3.25 and a previous upper bound of 46/7. We consider also the rotated two-dimensional mesh, in which the parallel jobs can be rotated and the rotation of all the jobs is feasible. A lower bound of 3.535 is proven and an on-line algorithm with competitive ratio of at most 4.25 is derived.