Graphs and algorithms
Static scheduling of synchronous data flow programs for digital signal processing
IEEE Transactions on Computers
Advances in Petri Nets 1988
Introduction to algorithms
Looped schedules for dataflow descriptions of multirate signal processing algorithms
Formal Methods in System Design
Rate-optimal schedule for multi-rate DSP computations
Journal of VLSI Signal Processing Systems - Special issue on application-specific array processors
The basic cyclic scheduling problem with linear precedence constraints
Discrete Applied Mathematics
Some complexity results in cyclic scheduling
Mathematical and Computer Modelling: An International Journal
Survey: Complexity of cyclic scheduling problems: A state-of-the-art survey
Computers and Industrial Engineering
Cyclic routing algorithms in graphs: Performance analysis and applications to robot scheduling
Computers and Industrial Engineering
Note: A note on periodic schedules for linear precedence constraints
Discrete Applied Mathematics
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We consider the computation of periodic cyclic schedules for linear precedence constraints graphs: a linear precedence constraint is defined between two tasks and induces an infinite set of usual precedence constraints between their executions such that the difference of iterations is a linear function. The objective function is the minimization of the maximal period of a task. We recall first that this problem may be modelled using linear programming. A polynomial algorithm is then developed to solve it for a particular class of linear precedence graphs called unitary graphs. We also show that a periodic schedule may not exist for unitary graphs. In the general case, a decomposition of the linear precedence graph into unitary components is computed and we assume that a periodic schedule exists for each of these components. Lower bounds on the periods are exhibited and we show that an optimal periodic schedule may not achieve them. The notion of quasi-periodic schedule is then introduced and we prove that this new class of schedules always reaches these bounds.