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
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
On-line scheduling of parallel jobs with runtime restrictions
Theoretical Computer Science
On an on-line scheduling problem for parallel jobs
Information Processing Letters
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Developments from a June 1996 seminar on Online algorithms: the state of the art
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Scheduling malleable tasks with precedence constraints
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Scheduling parallel jobs to minimize the makespan
Journal of Scheduling
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ACM Transactions on Algorithms (TALG)
A 5/4-approximation algorithm for scheduling identical malleable tasks
Theoretical Computer Science - Approximation and online algorithms
On-line scheduling mesh jobs with dependencies
Theoretical Computer Science
A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks
SIAM Journal on Computing
A scheduling algorithm for parallelizable dependent tasks
IPPS '91 Proceedings of the Fifth International Parallel Processing Symposium
Approximation algorithms for multiple strip packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Scheduling jobs on heterogeneous platforms
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Approximation algorithms for scheduling and packing problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
A(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
A (2+ε)-approximation for scheduling parallel jobs in platforms
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
A (5/3+ε )-approximation for strip packing
Computational Geometry: Theory and Applications
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In this paper we study variants of the nonpreemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most $(1+\varepsilon)\,\mathrm{OPT}$ can be calculated in polynomial time. Unless $P=NP$, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most $(1.5+\varepsilon)\,\mathrm{OPT}$ can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios.