Static task distribution

Example 6.1 Exploiting Data Locality in a Parallel Direct Hartree-Fock Program 

If we can determine in advance which tasks will be assigned to a given process, we can also predetermine what data that process will need to access. Hence, in some cases it may be possible to use a data distribution 

Distribution of tasks (labeled A-H) across three processes using a round-robin distribution. 

---

Superlinear speedups for Fock matrix formation in the iterative part of the Harlree-Fock procedure as a consequence of storing a larger fraction of the integrals on each process as the number of processes increases. Speedups for the entire Hartree-Fock procedure are shown as well. Computations were performed on a Linux cluster for the uracil dimer using the aug-cc-pVTZ basis set (cf. Figure 8.3). A static task distribution of atom quartets was employed (see section 8.3 for details of the algorithm). 

Outline of a simple round-robin static task distribution. The number of tasks is ntask/ P is the number of processes, and this proc is the process ID. 

The load imbalance resulting from a dynamic distribution of tasks is very difficult to model because the times required for the individual computational tasks are not known in advance. Provided that the number of tasks is much larger than the number of processes, however, it is reasonable to assume that the dynamic task distribution will enable an essentially even distribution of the load. For this to remain true as the number of processes increases, the number of tasks, umn, must increase proportionally to p. Although this is the same growth rate as obtained for a static work distribution, the actual value for umn needed for high efficiency for a given process count is much smaller for the dynamic distribution, and the assumption of perfect load balance is therefore adequate for our purposes. 

Processes request tasks (atom quartets) by calling the function get quartet, which has been implemented in both a dynamic and a static version. The dynamic work distribution uses a manager-worker model with a manager process dedicated to distributing tasks to the other processes, whereas the static version employs a round-robin distribution of tasks. When the number of processes is small, fhe sfafic scheme achieves the best parallel performance because the dynamic scheme, when run on p processes, uses only p - 1 processes for compulation. As the number of processes increases, however, the parallel performance for the dynamic task distribution surpasses that of the static scheme, whose efficiency is reduced by load imbalance. Wifh fhe entire Fock and density matrix available to every process, no communication is required during the computation of the Fock matrix other than the fetching of tasks in the dynamic scheme. After all ABCD tasks have been processed, a global summation is required to add the contributions to the Fock matrix from all processes and send the result to every process. 

The latter two components are responsible for distributing documents needed in the shared work process. The Starter/Static Replicator takes over that task upon startup it distributes the necessary documents to all parties and starts the shared program. During the work session, the Dynamic Replicator tracks the program run and distributes newly loaded documents to all sites. As a brief comparison. Fig. 3.51 summarizes the most important characteristics of application and event sharing. 

This chapter will focus on practicable methods to perform both the model specification and model estimation tasks for systems/models that are static or dynamic and linear or nonlinear. Only the stationary case win be detailed here, although the potential use of nonstationary methods will be also discussed briefly when appropriate. In aU cases, the models will take deterministic form, except for the presence of additive error terms (model residuals). Note that stochastic experimental inputs (and, consequently, outputs) may stiU be used in connection with deterministic models. The cases of multiple inputs and/or outputs (including multidimensional inputs/outputs, e.g., spatio-temporal) as well as lumped or distributed systems, will not be addressed in the interest of brevity. It will also be assumed that the data (single input and single output) are in the form of evenly sampled time-series, and the employed models are in discretetime form (e.g., difference equations instead of differential equations, discrete summations instead of integrals). 

The application program is divided into tasks, and the distribution of the application-level functions among the tasks is static. Each task has a special role, and the most important tasks are. 

The other task allocation scheme, static load balancing, does not require any interprocessor communication, but distributes... 

---