Algorithms and analysis of scheduling for loops with minimum switching

Abstract

Switching activity and schedule length are the two of the most important factors in power dissipation. This paper studies the scheduling problem that minimizes both schedule length and switching activities for applications with loops on multiple-functional-unit architectures. We show that to find a schedule that has the minimal switching activities among all minimum-latency schedules with or without resource constraints is NP-complete. Although the minimum latency scheduling problem is polynomial-time solvable if there is no resource constraints or only one functional unit(FU), the problem becomes NP-complete when switching activities are considered as the second constraint. An algorithm, Power Reduction Rotation Scheduling (PRRS), is proposed. The algorithm attempts to minimize both switching activities and schedule length while performing scheduling and allocation simultaneously. Compared with the list scheduling, PRRS shows an average 20.1% reduction in schedule length and 52.2% reduction in bus switching activities. Our algorithm also shows better performance than the approach that considers scheduling and allocation at separate phases.

Optimal Scheduling of Urgent Preemptive Tasks

“…In fact, Mok showed that the scheduling problem for real-time systems with shared resources and no knowledge about the future start times of the tasks is undecidable [24]. It is important in practice to reduce task waiting time and context-switching time, especially when power dissipation is considered [19], [27]. However, for simiplicity Definition 2.1 assumes also that there is no context-switching time.…”

Energy-Aware Loop Scheduling and Assignment for Multi-Core, Multi-Functional-Unit Architecture

“…Then based on the precedence relation in the retimed graph G r , we rotate each node u ∈ U r by putting u into the location with the minimum switching activities among all available empty locations in LOC, where LOC is the set containing all available locations of u. We obtain the best location for a rotated node by the following strategy [12]. For a location [i, j ] ∈ LOC, we define a function, SL(u, [i, j ]), to compute the switching activities if u is assigned to location [i, j ].…”

“…According to [12], the instruction-level energyminimization scheduling is NP-complete with or without resource constraints. In the paper, we design an algorithm, EMPLS (Energy Minimization with Probability using Loop Scheduling), to minimize total energy (E p + E s ) while satisfying timing constraint with guaranteed probability for loop applications by performing scheduling and assignment simultaneously.…”

“…In the EMPLS algorithm, the schedules are generated by repeatedly rotating down and re-allocating nodes with minimum total energy (E p + E s ) based on rotation scheduling [35], and a best schedule and assignment is selected that has the minimal total energy (E p + E s ) among all schedules and assignments while satisfying timing constraint with guaranteed probability. Compared with algorithms in [12], our algorithm has two advantages: 1) our algorithm can find solutions with smaller total energy even for hard real-time situation. 2) it is able to provide a larger solution space that results in smaller total energy consumption while satisfying timing constraint with guaranteed probability.…”

“…2) it is able to provide a larger solution space that results in smaller total energy consumption while satisfying timing constraint with guaranteed probability. While algorithm [12] may not find solution with certain timing constraints.…”