Fine-grain scheduling under resource constraints

In high-level synthesis, loop pipelining is a technique to improve the throughput and utilisation of hardware datapaths by starting new loop iterations after a fixed amount of time, called the initiation interval (II), allowing to overlap subsequent iterations. The problem is to find the smallest II and corresponding operation schedule that fulfils all data dependencies and resource constraints, both of which are usually found by modulo scheduling.We propose Moovac1, a novel integer linear program (ILP) formulation of the modulo scheduling problem based on overlap variables to model exact resource constraints. Given enough time, Moovac will find a mimimum-II solution. This is in contrast to Canis' state-of-the-art Modulo SDC approach, which requires heuristic simplifications of the resource constraints. Moovac can thus be used as a reference to evaluate heuristics, or in a time-limited mode as a heuristic itself to provide a best-so-far solution.We schedule kernels from the CHStone and MachSuite benchmarks for loop pipelining with Moovac, Modulo SDC and a prior exact formulation by Eichenberger.Moovac has competitive performance in its time-limited mode, and delivers better results faster than the Modulo SDC scheduler for some loops. Often its structure leads to quicker solution times than Eichenberger's formulation.Using the Moovac-computed optimal solutions as a reference, we can confirm that the Modulo SDC heuristic is indeed capable of finding optimal or near-optimal solutions for the majority of small- to medium-sized loops. However, for larger loops the two algorithms begin to diverge, with Moovac often being significantly faster to prove the infeasibility of a candidate II. This can be exploited by running both schedulers synergistically, leading to a quicker convergence to the final II.

This paper presents several theoretical and fundamental results on the register need in periodic schedules, also known as MAXLIVE. Our first contribution is a novel formula for computing the exact number of registers needed by a scheduled loop. This formula has two advantages: Its computation can be done by using a polynomial algorithm with O(n lg n) complexity (n is the number of instructions in the loop) and it allows the generalization of a previous result [13]. Second, during software pipelining, we show that the minimal number of registers needed may increase when incrementing the initiation interval (II), which is contrary to intuition. For the case of zero architectural delays in accessing registers, we provide a sufficient condition for keeping the minimal number of registers from increasing when incrementing the II. Third, we prove an interesting property that enables us to optimally compute the minimal periodic register sufficiency of a loop for all its valid periodic schedules, irrespective of II. Fourth and last, we prove that the problem of optimal stage scheduling under register constraints is polynomially solvable for a subclass of data dependence graphs, whereas this problem is known to be NP-complete for arbitrary dependence graphs [7]. Our latter result generalizes a previous achievement [13] which addressed data dependence trees and forest of trees. In this study, we consider cyclic data dependence graphs without taking into account any resource constraints. The aim of our theoretical results on the periodic register need is to help current and future software pipeliners achieve significant performance improvements by making better (if not the best) use of the available resources.

Release planning is a cornerstone problem in incremental software development. It deals with the assignment of requirements to sequence of releases in order to maximize profit, minimize the delay of feedback and return of investment in such a way that dependency and resource constraints are met. Release planning decisions are required at an early stage in the development cycle, when uncertainty is unavoidable in the project estimates. Recently, there are some works concerning the use of fuzzy theory to address issues concerning the uncertainty in the release planning problem: fuzzy effort constraints and fuzzy dependency constraints. In this paper, we study the application of fuzzy theory to handle the uncertainty concerning dependency constraints from a holistic perspective, i.e. the whole set of fuzzy dependency constraints is considered as a fuzzy graph. The satisfaction of dependency constraints in a solution plan is measured by the distance between this plan and an ideal plan (in terms of the dependency constraints). The distance is materialized as the distance between two fuzzy graphs. This is considered to be an essential support for the actual decision-making. All the concepts and the complete approach are illustrated by a case study example.

This paper introduces a new static data dependence constraint, called dependence difference inequality, which can deal with coupled subscripts for multi-dimensional array references. Unlike direction vectors, dependence difference inequalities are related to not only the iteration space for a loop program but also the operation distance between two operations. They are more strict than other methods, and can act as additional constraints to each variable in a linear system on their own or with others. As a result, the solution space for a linear system can be compressed heavily. So long as dependence difference inequalities do not satisfy simultaneously, the loop can be software-pipelined with any initiation interval even if there exists a data dependence between two operations. Meanwhile, by replacing direction vectors with dependence difference inequalities some conservative estimations made by other traditional data dependence analysis approaches can be eliminated.

The performance of pipelined datapath implementations is measured basically by three parameters: the clock cycle length, the initiation interval between successive iterations (inverse of the throughput) and the iteration time (turn-around time). In this paper we present a new method for computing performance bounds of pipelined implementations: The method has a low complexity and it handles behavioral specifications containing loop statements with interiteration data dependency and timing constraints.

Linear difference equations involving recurrences are fundamental equations that describe many important signal processing applications. For many high sample rate digital filter applications, it is necessary to effectively parallelize the linear difference equations used to describe digital filters. This is difficult because of the recurrences inherent in the data dependences. The authors present a novel approach, harmonic scheduling, that exploits parallelism in these recurrences beyond loop-carried dependencies, and which generates optimal schedules for parallel evaluation of linear difference equations with resource constraints. This approach also enables the derivation of a parallel schedule with minimum control overhead, given an execution time with resource constraints. A harmonic scheduling algorithm is presented to generate optimal schedules for digital filters described by second-order difference equations with resource constraints. >

Literature suggests that both the government and professional bodies are supportive of role development and changing of professional boundaries, but is this representative of current clinical practice? All 97 mainland UK National Health Service Breast Screening Programme (NHSBSP) centres were surveyed. Postal questionnaires were sent to both radiographer film readers and departmental superintendent radiographers centring on practical, clinical and managerial issues concerning the current practice and implementation of extended roles. An overall response rate of 79% was achieved. Of radiographers working in breast screening, 10% are trained in image interpretation and reporting in mammography. Only 43% of these read annually a minimum of 5,000 mammograms – the quality guidelines for radiologists. Many barriers inhibiting the utilisation of radiographer film readers were identified: 1. Resource constraints, both human and financial 2. Time constraints 3. Quality assurance issues 4. National structure. This study demonstrated under-utilisation of radiographer film readers in the UK NHSBSP, raising the issue of 'Is training radiographers to film read an efficient and effective use of scarce health care resources?' Further research into this contentious issue is necessary to fully evaluate and ensure effective use of clinical skills; better service to the patient; and efficient use of health care resources is undertaken.

Real-time embedded systems are typically constrained in terms of three system performance criteria: space, time, and energy. The performance requirements are directly translated into constraints imposed on the system's resources, such as code size, execution time, and energy consumption. These resource constraints often interact or even conflict with each other in a complex manner, making it difficult for a system developer to apply a well-defined design methodology in developing a real-time embedded system. Motivated by this observation, we propose a design framework that can flexibly balance the tradeoff involving the system's code size, execution time, and energy consumption. Given a system specification and an optimization criteria, the proposed technique generates a set of design parameters in such a way that a system cost function is minimized while the given resource constraints are satisfied. Specifically, the technique derives code generation decision for each task so that a specific version of code is selected among a number of different ones that have distinct characteristics in terms of code size and execution time. In addition, the design framework determines the voltage/frequency setting for a variable voltage processor whose supply voltage can be adjusted at runtime in order to minimize the energy consumption while execution performance is degraded accordingly. The proposed technique formulates this design process as a constrained optimization problem. We show that this optimization problem is NP-hard and then provide a heuristic solution to it. We show that these seemingly conflicting design goals can be pursued by using a simple optimization algorithm that works with a single optimization criteria. Moreover, the optimization is driven by an abstract system specification given by the system developer, so that the system development process can be automated. The results from our simulation show that the proposed algorithm finds a solution that is close to the optimal one with the average error smaller than 1.0%.

The resource constrained time/cost tradeoff project scheduling problem with discounted cash flows

An Integrated Practice Unit (IPU) is a new approach to outpatient care in which a co-located multidisciplinary team of clinicians, technicians, and staff provide treatment in a single patient visit. This article presents a new integer programming model for an extended open shop problem with application to clinic appointment scheduling for IPUs. The advantages of the new model are discussed and several valid inequalities are introduced to tighten the linear programming relaxation. The objective of the problem is to minimize a combination of makespan and total job processing time, or in terms of an IPU, to minimize a combination of closing time and total patient waiting time. Feasible solutions are obtained with a two-step heuristic, which also provides a lower bound that is used to judge solution quality. Next, a two-stage stochastic optimization model is presented for a joint pain IPU. The expected value solution is used to generate two different patient arrival templates. Extensive computations are performed to evaluate the solutions obtained with these templates and several others found in the literature. Comparisons with the expected value solution and the wait-and-see solution are also included. For the templates derived from the expected value solution, the results show that the average gap between the feasible solution and lower bound provided by the two-step heuristic is 2% for 14 patients. They also show that either of the two templates derived from the expected value solution is a good candidate for assigning appointment times when either the clinic closing time or the patient waiting time is the more important consideration. Sensitivity analysis confirmed that the optimality gap and clinic statistics are stable for marginal changes in key resources.

Loops are the main source of parallelism in scientific programs. Hence, several techniques were developed to detect parallelism in these loops and transform them into parallel forms. In this dissertation, compile time transformations and efficient parallel execution of loops with various type of dependencies are investigated. First, Doacross loops with uniform dependencies are considered for execution on distributed memory parallel machines (multicomputers). Most known Doacross loop execution techniques can be applied efficiently only to shared memory parallel machines. In this thesis, code reordering technique, improvements to partitioning strategies, and finding a balance between communication and parallelism are presented to reduce the execution time of Doacross loops on multicomputers. As with most parallelizing transformation techniques, only single loopnests are considered in the first part of this dissertation. However, parallelizing each loopnest in a program separately, even if an optimal execution can be obtained for each loopnest, may not result in an efficient execution of all the code in the program because of communication overhead across the loops in a multicomputer environment. Hence, across loop data dependence representation and analysis are introduced in this work to improve the parallel execution of the whole code. Our contribution consists of finding and representing data dependencies whose sources and destinations are subspaces of the iteration space mainly common across the loops. This type of dependence information is used in this thesis to improve global iteration space partitioning, automatic generation of communication statements across loops, and index alignment. The final part of this dissertation presents new parallelizing techniques for loops with irregular and complex dependencies. Various data dependence analysis algorithms can be found in the literature even for loops with complex array indexing. However, the improvement in data dependence testing has not been followed by similar amelioration in restructuring transformations for loops with complex dependencies. Such loops are mostly executed in serial mode. Our parallelizing techniques for these loops consists of identifying regions of the iteration space where all iterations can be executed in parallel. The advantages of all the transformations presented in this dissertation are: (1) they significantly reduce the execution time of loops with various types of dependencies as shown in this work using the MasPar machine (2) they can be implemented at compile, time which makes the task of parallel programming easier.

Data dependence uniformization, a method for overcoming the difficulties in parallelizing a doubly nested loop with irregular dependence constraints is proposed. This approach is based on the concept of vector decomposition. A simple set of basic dependences is developed from which all dependence constraints can be composed. The set of basic dependences is added to every iteration to replace all original dependences so that the dependence constraints become uniform. An efficient synchronization method is presented to obey the uniform dependence constraints in every iteration. >

A branch-and-price approach for the nurse rostering problem with multiple units

Task assignment optimization in geographically distributed data centers

In this chapter we address the problem of mapping a biochemical application modeled as a sequencing graph to a given biochip architecture. The mapping consists of the binding, scheduling, and routing tasks. We first propose a constraint programming (CP) synthesis approach that optimally synthesizes a biochemical application onto the specified biochip architecture with the application completion time minimization as the target objective. The synthesis process involves performing binding and scheduling of operations while satisfying the dependency and resource constraints. Our CP approach ignores fluid routing. We also propose a computationally efficient heuristic approach that also takes into account fluidic routing (contention aware edge scheduling) together with the operation mapping. Real-life case studies and a set of synthetic benchmarks have been synthesized on different architectures for validating the proposed approach. To aid the development and testing during the application development phase, we have also developed a simulator that shows how a given mapped biochemical application is executed on a target biochip architecture. The proposed approaches are expected to reduce human effort, enabling designers to take early design decisions by being able to evaluate their proposed architecture, minimizing the design cycle time and also facilitating programmability and automation.