Geometry and topology for mesh generation by Herbert Edelsbrunner

By Herbert Edelsbrunner

This e-book combines arithmetic (geometry and topology), laptop technological know-how (algorithms), and engineering (mesh new release) in an effort to resolve the conceptual and technical difficulties within the combining of components of combinatorial and numerical algorithms. The ebook develops tools from components which are amenable to mix and explains fresh leap forward recommendations to meshing that healthy into this classification. it may be a terrific graduate textual content for classes on mesh new release. the explicit fabric is chosen giving choice to issues which are ordinary, appealing, lend themselves to educating, are important, and engaging.

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We proved theoretically that the method converges to the global optimum. We also presented examples where our algorithm actually gives better solutions than the solutions given by the state-of-the-art heuristics which explore the index configuration space. The method does not require any phase for preparatory candidate index selection. In addition it shows very low sensitivity to parameter settings, therefore it can be especially useful in the implementations of self-tuning, autonomic database systems.

7 Convergence curves for the TPC-H workload Fig. 8 Estimated costs of TPC-H workload as a function of the storage space limit We have also checked how the plan selection algorithm affects the performance of the method. As a reference, we have implemented the uniform plan selection algorithm. The proportional selection gave much better average results over the uniform selection (Fig. 5). When using the uniform selection, sometimes running even 100,000 iterations did not produce optimal results. The best recorded convergence curve for the uniform selection was also much worse than that for the proportional selection (Fig.

The recommended index sets and their estimated benefits were similar, but not exactly the same in both solutions. The observed differences were presumably caused by the query plan cost models that did not exactly match. Materializing the indexes recommended by our tool for the storage size limit of 40%, applied for the DB/2 database, improved the estimated workload cost by over 55%, but obviously not as much as the original DB/2 recommendation. The same situation was observed when applied the DB/2 recommendation to our cost model — the value of the objective function was better for our solution than for the DB/2 advisor’s one.

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