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124 6 ⋅ software The most complicated piece of the interface is the csr_graph object. This object is itself a generic object because it must support both 64-bit and 32-bit index types on the compressed sparse row arrays. Furthermore, it supports an optimization for algorithms that do not require edge weights. We will not delve into its implementation here as the arcana of implementing a Boost graph concept are best left to the Boost graph documentation.7 copy-free? A key feature of MatlabBGL is that it provides large-scale graph algorithms in Matlab by avoiding copies. However, the first step in almost every algorithm is to copy and transpose the sparse matrix. For true large-scale computations, users must take care to ensure that the no-copy computation paths within MatlabBGL are used. Most MatlabBGL functions support these paths and exceptional cases are all documented.8 6.3.3 libmbgl: A compressed sparse row interface Within MatlabBGL, libmbgl is the component that translates a compressed- sparse row graph representation into a BGL graph type and makes the BGL function call. As figure 6.2 reflects, this library is completely independent of the Matlab components. One of the reasons for this separation is that libmbgl provides a fast interface to the Boost graph library from any application that can link against a set of C functions. We are aware of at least one manuscript where this lower level interface was used [Karci, 2008]. Furthermore, libmbgl opens the possibility to reuse a piece of MatlabBGL with open source scientific computing packages such as SciLab and Octave. If these libraries provide access to a compressed row representation, then libmbgl provides the necessary link. MatlabBGL is mostly usable “as-is” in the Octave program because they implement the Matlab mex interface and support a rough equivalent to the Matlab language. In summary, we consider libmbgl an integral, but independent, piece of MatlabBGL and plan to keep it that way. 6.3.4 Return types Thus far, we’ve seen how MatlabBGL takes a sparse matrix and translates it to a function call in the Boost graph library. Next, the Boost graph library generally computes a result as part of this function call. We need to represent these results in Matlab. Recall that one of the design philosophies of MatlabBGL is to add as little to Matlab as possible. With this constraint, picking amongst options for the return types is straightforward. Algorithms that compute a metric on a vertex, such as strong_components or clustering_coefficients, already support writing data to a standard int* or double* array. The wrappers in libmbgl return these data to the mex functions, which proceed to store them in Matlab arrays.9 For measures on edges, such as biconnected_components, we often sup- port two different return value mechanisms. When the values are all non-zero, MatlabBGL will return a sparse matrix with the edge information. When the 7 It is interesting to note that the first version of MatlabBGL with an entirely correct Graph concept was the third iter- ation of the library. Earlier revisions did not implement an obscure property that was eventually used in the dominator_¬ tree algorithm. 8 Presently, the exceptional cases are the maximum flow routines and the planar graph triangulation function. 9 Because libmbgl requires the array stor- age to be allocated before the function call, the data are stored directly into the Matlab arrays when possible.PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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