Approximation Algorithm for Scheduling a Chain of Tasks on Heterogeneous Systems

Abstract

This paper presents an efficient approximation algorithm to solve the task scheduling problem on heterogeneous platform for the particular case of the linear chain of tasks. The objective is to minimize both the total execution time (makespan) and the total energy consumed by the system. For this purpose, we introduce a constraint on the energy consumption during execution. Our goal is to provides an algorithm with a performance guarantee. Two algorithms have been proposed; the first provides an optimal solution for preemptive scheduling. This solution is then used in the second algorithm to provide an approximate solution for non-preemptive scheduling. Numerical evaluations demonstrate that the proposed algorithm achieves a close-to-optimal performance compared to exact solution obtained by CPLEX for small instances. For large instances, CPLEX is struggling to provide a feasible solution, whereas our approach takes less than a second to produce a solution for an instance of 10000 tasks.

Efficient exact algorithms for continuous bi‐objective performance‐energy optimization of applications with linear energy and monotonically increasing performance profiles on heterogeneous high performance computing platforms

“…Tarplee et al 26 employ task‐mapping as a decision variable for bi‐objective optimization of applications for performance and energy in a HPC platform. Aba et al 27 present an approximation algorithm for bi‐objective optimization of parallel applications running on a heterogeneous resources system for performance and total energy. The decision variable is task scheduling.…”

Tice: A real‐time language compilable using C++ compilers

“…The semantics of the end‐to‐end delay that Tice can enforce is called last‐to‐first according to the nomenclature that is introduced by Feiertag et al 31 To our knowledge the semantics of correlation has not been explored to the same extent that permits us to name the semantics of Tice's correlation constraint in the same manner. Other possible semantics of end‐to‐end delay has been further studied by Forget et al in proposing a language to express end‐to‐end delay constraints with various semantics as well as the framework to verify the expressed constraints on the multiperiodic synchronous MoCC of Prelude , 59 while Khatib et al 60 and Aba et al 61 investigate end‐to‐end delay in a synchronous dataflow graph and in minimizing a system's energy consumption, respectively. Aside from that, while different strategies exist to implement the LET MoCC depending on the target hardware and the optimality criteria, 57,62,63 currently Tice library uses a simplistic nonoptimal implementation strategy described in Sections 6.1 and 6.2 while showing how to accommodate other implementation strategies in Section 6.3.…”