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
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
An approximation algorithm for scheduling malleable tasks under general precedence constraints
ACM Transactions on Algorithms (TALG)
A $\frac32$-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks
SIAM Journal on Computing
Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Tightness results for malleable task scheduling algorithms
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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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 (1991, 1994, 1996) [23-25], 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. 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 asymptotically tight.