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imaginary part of C on the vertical axis and the real part on the horizontal axis The color of each pixel is black if the recurrence relation converges to a stable value or is colored depending on how rapidly the relation diverges At the lowest level, the task is the update for a single pixel First consider computing this set on a cluster of PCs connected by an Ethernet This is a coarsegrained system; that is, the rate of communication is slow relative to the rate of computation To offset the overhead incurred by the slow network, the task size needs to be large; for this problem, that might mean computing a full row of the image The work involved in computing each row varies depending on the number of divergent pixels in the row The variation, however, is modest and distributed closely around a mean value Therefore, a static schedule with many more tasks than UEs will likely give an effective statistical balance of the load among nodes The remaining step in applying the pattern is choosing an overall structure for the program On a shared memory machine using OpenMP, the Loop Parallelism pattern described in the Supporting Structures design space is a good fit On a network of workstations running MPI, the SPMD pattern (also in the Supporting Structures design space) is appropriate Before moving on to the next example, we consider one more target system, a cluster in which the nodes are not heterogeneous that is, some nodes are much faster than others Assume also that the speed of each node may not be known when the work is scheduled Because the time needed to compute the image for a row now depends both on the row and on which node computes it, a dynamic schedule is indicated This in turn suggests that a general dynamic load balancing scheme is indicated, which then suggests that the overall program structure should be based on the Master/Worker pattern.

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For our second example, we consider the computation of the nonbonded forces in a molecular dynamics computation This problem is described in Sec 313 and in [Mat95, PH95] and is used throughout the patterns in the Finding Concurrency design space Pseudocode for this computation is shown in Fig 44 The physics in this example is not relevant and is buried in code not shown here (the computation of the neighbors list and the force function) The basic computation structure is a loop over atoms, and then for each atom, a loop over interactions with other atoms The number of interactions per atom is computed separately when the neighbors list is determined This routine (not shown here) computes the number of atoms within a radius equal to a preset cutoff distance The neighbor list is also modified to account for Newton's third law: Because the force of atom i on atom j is the negative of the force of atom j on atom i, only half of the potential interactions need actually be computed Understanding this detail is not important for understanding this example The key is that this causes each loop over j to vary greatly from one atom to another, thereby greatly complicating the load balancing problem Indeed, for the purposes of this example, all that must really be understood is that calculating the force is an expensive operation and that the number of interactions per atom varies greatly Hence, the computational effort for each iteration over i is difficult to predict in advance

All attribute values in SimpleDB are stored as raw character stringsThis eliminates the work and deployment headaches of rolling out cluster-wide schema changes However, the lack of a robust set of data types has serious implications for data formatting and queries The issue with string data, with regard to queries, is the way comparisons are performed, alphabetically from left to right For instance, the following two names sort correctly, even though they are different lengths:

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