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Abstract. Stream (data-flow) computing is considered an effective paradigm for parallel programming of high-end multi-core architectures for embedded applications (networking, multimedia, wireless communication). Our work addresses a key step in stream programming for embedded multicores, namely, the efficient mapping of a synchronous data-flow graph (SDFG) onto a multi-core platform subject to a minimum throughput requirement. This problem has been extensively studied in the past, and its complexity has lead researches to develop incomplete algorithms which cannot exclude false negatives. We developed a CP-based complete algorithm based on a new throughput-bounding constraint. The algorithm has been tested on a number of non-trivial SDFG mapping problems with promising results.

Abstract.A cyclic scheduling problem is specified by a set of activities that are executed an infinite number of times subject to precedence and resource constraints. The cyclic scheduling problem has many applications in manufacturing, production systems, embedded systems, compiler design and chemical systems. This paper proposes a Constraint Programming approach based on Modular Arithmetic, taking into account temporal resource constraints. In particular, we propose an original modular precedence constraint along with its filtering algorithm. Classical "modular" approaches that fix the modulus and solve an integer linear sub-problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model that faces the problem as a whole: the modulus domain bounds are inferred from the activity-related and iteration-related variables. The method has been extensively tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances. Both the time to compute a solution and its quality have been assessed. The method is extremely fast to find close to optimal solutions in a very short time also for large instances. In addition, we have found a solution for one instance that was previously unsolved and improved the bound of another of a factor of 11.5%.

Abstract. In the context of Scheduling under uncertainty, Partial Order Schedules (POS) provide a convenient way to build flexible solutions. A POS is obtained from a Project Graph by adding precedence constraints so that no resource conflict can arise, for any possible assignment of the activity durations. In this paper, we use a simulation approach to evaluate the expected makespan of a number of POSs, obtained by solving scheduling benchmarks via multiple approaches. Our evaluation leads us to the discovery of a striking correlation between the expected makespan and the makespan obtained by simply fixing all durations to their average. The strength of the correlation is such that it is possible to disregard completely the uncertainty during the schedule construction and yet obtain a very accurate estimation of the expected makespan. We provide a thorough empirical and theoretical analysis of this result, showing the existence of solid ground for finding a similarly strong relation on a broad class of scheduling problems of practical importance.

Abstract. Weighted average expressions frequently appear in the context of allocation problems with balancing based constraints. In combinatorial optimization they are typically avoided by exploiting problems specificities or by operating on the search process. This approach fails to apply when the weights are decision variables and when the average value is part of a more complex expression. In this paper, we introduce a novel average constraint to provide a convenient model and efficient propagation for weighted average expressions appearing in a combinatorial model. This result is especially useful for Empirical Models extracted via Machine Learning (see [2]), which frequently count average expressions among their inputs. We provide basic and incremental filtering algorithms. The approach is tested on classical benchmarks from the OR literature and on a workload dispatching problem featuring an Empirical Model. In our experimentation the novel constraint, in particular with incremental filtering, proved to be even more efficient than traditional techniques to tackle weighted average expressions.