By Ruy Luiz Milidiú, Artur Alves Pessoa, Eduardo Sany Laber (auth.), Michael T. Goodrich, Catherine C. McGeoch (eds.)

Symmetric multiprocessors (SMPs) dominate the high-end server marketplace and are at present the first candidate for developing huge scale multiprocessor structures. but, the layout of e cient parallel algorithms for this platform c- rently poses a number of demanding situations. the reason is, the speedy growth in microprocessor velocity has left major reminiscence entry because the fundamental problem to SMP functionality. due to the fact that reminiscence is the bottleneck, easily expanding the n- ber of processors won't inevitably yield higher functionality. certainly, reminiscence bus barriers mostly restrict the scale of SMPs to sixteen processors. This has at the very least twoimplicationsfor the algorithmdesigner. First, seeing that there are fairly few processors availableon an SMP, any parallel set of rules has to be aggressive with its sequential counterpart with as low as one processor to be able to be r- evant. moment, for the parallel set of rules to scale with the variety of processors, it needs to be designed with cautious awareness to minimizing the quantity and kind of major reminiscence accesses. during this paper, we current a computational version for designing e cient al- rithms for symmetric multiprocessors. We then use this version to create e cient options to 2 greatly di erent different types of difficulties - associated checklist pre x com- tations and generalized sorting. either difficulties are reminiscence in depth, yet in die lease methods. while generalized sorting algorithms in general require a wide numberofmemoryaccesses, they areusuallytocontiguousmemorylocations. against this, prex computation algorithms normally require a extra modest qu- tity of reminiscence accesses, yet they're tend to be to non-contiguous reminiscence locations.

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Operation counts and the observer technique enabled us to explain these observations. It was also somewhat unexpected how much more difficult problems on the lowest density level turned out to be. However, this corresponds to a much higher number of blossom shrinking operations and a larger nesting level. Blossom shrinking is expensive but unfortunately a simple heuristic to reduce the number of shrinking steps is only successful for extremely sparse graphs which turned out to be the most difficult problem instances.

Gabow, An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems, Proceedings of the 15th Annual ACM Symposium on the Theory of Computing (1983), 448–456. Ger95. A. M. H. Gerards, Matching, Handbooks in Operations Research and Management Science, vol. 7, North-Holland, 1995, pp. 135–224. GH85. M. Gr¨ otschel and O. Holland, Solving matching problems with linear programming, Math. Prog. 33 (1985), 243–259. Mar79. A. B. D. thesis, The John Hopkins University, Baltimore, 1979.

1. Real-world data: mesh refinement As mentioned in the introduction, a successful approach to CAD mesh refinement into quadrilateral finite element meshes requires the solution of minimum cost perfect b-matching problems as a subroutine. We selected all available instances with non-trivial size (more than 3000 nodes) for our test-suite. These instances are extremely sparse, 24 M. M¨ uller–Hannemann, A. 6. 2. Synthetic data: Euclidean nearest-neighbor graphs We produce an artificial b-matching problem instance as follows, parameterized by the number of nodes n, the density d = m/n, and the node capacities bmax .