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Problem How can an algorithm be organized around a data structure that has been decomposed into concurrently updatable "chunks" Context Many important problems are best understood as a sequence of operations on a core data structure There may be other work in the computation, but an effective understanding of the full computation can be obtained by understanding how the core data structures are updated For these types of problems, often the best way to represent the concurrency is in terms of decompositions of these core data structures (This form of concurrency is sometimes known as domain decomposition, or coarse grained data parallelism) The way these data structures are built is fundamental to the algorithm If the data structure is recursive, any analysis of the concurrency must take this recursion into account For recursive data structures, the Recursive Data and Divide and Conquer patterns are likely candidates For arrays and other linear data structures, we can often reduce the problem to potentially concurrent components by decomposing the data structure into contiguous substructures, in a manner analogous to dividing a geometric region into subregions hence the name Geometric Decomposition For arrays, this decomposition is along one or more dimensions, and the resulting subarrays are usually called blocks We will use the term chunks for the substructures or subregions, to allow for the possibility of more general data structures, such as graphs This decomposition of data into chunks then implies a decomposition of the update operation into

The earlier section on the WHERE clause briefly alluded to predicates and the comparisons within themThis section offers a more thorough dissection of this important area A predicate is the set of comparisons made for a given attribute within the WHERE clause Here is an example of a single predicate with a single comparison:

StringWriter() creates a new string writer, using the default-sized buffer StringWriter(int startingSize) creates a new string writer and allocates a StringBuffer of the specified size

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tasks, where each task represents the update of one chunk, and the tasks execute concurrently If the computations are strictly local, that is, all required information is within the chunk, the concurrency is embarrassingly parallel and the simpler Task Parallelism pattern should be used In many cases, however, the update requires information from points in other chunks (frequently from what we can call neighboring chunks chunks containing data that was nearby in the original global data structure) In these cases, information must be shared between chunks to complete the update

WHERE date LIKE '200%'

StringBuffer getBuffer() returns the buffer used to store data sent to the String toString() converts the internal buffer into a string

The problem is to model 1D heat diffusion (that is, diffusion of heat along an infinitely narrow pipe) Initially, the whole pipe is at a stable and fixed temperature At time 0, we set both ends to different temperatures, which will remain fixed throughout the computation We then calculate how temperatures change in the rest of the pipe over time (What we expect is that the temperatures will converge to a smooth gradient from one end of the pipe to the other) Mathematically, the problem is to solve a 1D differential equation representing heat diffusion: Equation 42

4475 OutputStreamWriter Class While there are many writer classes equivalent to output stream classes in the Java API, there is still a need to maintain compatibility with older output stream classes, as most of the networking API and some third-party libraries provide only stream interfaces The OutputStreamWriter class handles the translation between a Writer and an OuputStream, allowing new writer classes to interact with older output streams Constructors

Multiple comparisons for the same attribute are combined into the same predicate For example:

The approach used is to discretize the problem space (representing U by a one dimensional array and computing values for a sequence of discrete time steps) We will output values for each time step as they are computed, so we need only save values for U for two time steps; we will call these arrays uk (U at the timestep k) and ukp1 (U at timestep k + 1) At each time step, we then need to compute for each point in array ukp1 the following:

OutputStreamWriter(OutputStream output, String encoding) throws javaioUnsupportedEncodingException creates a writer that translates

WHERE date LIKE '200%' OR date > '1989'

ukp1[i]=uk[i]+ (dt/(dx*dx))*(uk[i+1]-2*uk[i]+uk[i-1]);

between characters and bytes, using the specified character encoding If the specified encoding form is not supported, an exception is thrown Methods The OutputStreamWriter class adds the following public method:

OutputStreamToWriter Example The example below demonstrates how a writer may be connected to an output stream by using the extremely compact, and doesn't require much effort Code for OutputStreamToWriterDemo

Variables dt and dx represent the intervals between discrete time steps and between discrete points, respectively Observe that what is being computed is a new value for variable ukp1 at each point, based on data at that point and its left and right neighbors We can begin to design a parallel algorithm for this problem by decomposing the arrays uk and ukp1 into contiguous subarrays (the chunks described earlier) These chunks can be operated on concurrently, giving us exploitable concurrency Notice that we have a situation in which some elements can be updated using only data from within the chunk, while others require data from neighboring chunks, as illustrated by Fig 48

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