Scheduling precedence graphs in systems with interprocessor communication times
SIAM Journal on Computing
Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Generalised multiprocessor scheduling using optimal control
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
LogP: a practical model of parallel computation
Communications of the ACM
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Scheduling malleable and nonmalleable parallel tasks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Linear-time approximation schemes for scheduling malleable parallel tasks
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
List scheduling of general task graphs under LogP
Parallel Computing - Special issue on new trends on scheduling in parallel and distributed systems
Parallel Computer Architecture: A Hardware/Software Approach
Parallel Computer Architecture: A Hardware/Software Approach
Generalized multiprocessor scheduling for directed acylic graphs
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Dynamic Load Balancing for Ocean Circulation Model with Adaptive Meshing
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial-Time Approximation Scheme
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Strip packing with precedence constraints and strip packing with release times
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ACM Transactions on Algorithms (TALG)
Strip packing with precedence constraints and strip packing with release times
Theoretical Computer Science
Online scheduling of malleable parallel jobs
PDCS '07 Proceedings of the 19th IASTED International Conference on Parallel and Distributed Computing and Systems
Improved results for scheduling batched parallel jobs by using a generalized analysis framework
Journal of Parallel and Distributed Computing
Provably efficient two-level adaptive scheduling
JSSPP'06 Proceedings of the 12th international conference on Job scheduling strategies for parallel processing
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
Scheduling moldable tasks for dynamic SMP clusters in soc technology
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Hierarchical scheduling for moldable tasks
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
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In this paper we propose an approximation algorithm for scheduling malleable tasks with precedence constraints. Based on an interesting model for malleable tasks with continuous processor allotments by Prasanna and Musicus [22, 23, 24], we define two natural assumptions for malleable tasks: the processing time of any malleable task is non-increasing in the number of processors allotted, and the speedup is concave in the number of processors. We show that under these assumptions the work function of any malleable task is non-decreasing in the number of processors and is convex in the processing time.Furthermore, we propose a two-phase approximation algorithm for the scheduling problem. In the first phase we solve a linear program to obtain a fractional allotment for all tasks. By rounding the fractional solution, each malleable task is assigned a number of processors. In the second phase a variant of the list scheduling algorithm is employed. In the phases we use two parameters μ ∈{1... ⌊ (m+1)/2⌋} and ρ ∈ [0,1] for the allotment and the rounding, respectively, where m is the number of processors. By choosing appropriate values of the parameters, we show (via a nonlinear program) that the approximation ratio of our algorithm is at most 100/63+100(√6469+13)/5481 ≈ 3.291919. We also show that our result is very close to the best asymptotic one.