No abstract

In the early stage of floorplan design, many modules have large flexibilities in shape (soft modules). Handling soft modules in general nonslicing floorplan is a complicated problem. Many previous works have attempted to tackle this problem using heuristics or numerical methods, but none of them can solve it optimally and efficiently. In this paper, we show how this problem can be solved optimally by geometric programming using the Lagrangian relaxation technique. The resulting Lagrangian relaxation subproblem is so simple that the optimal size of each module can be computed in linear time. We implemented this method in a simulated annealing framework based on the sequence pair representation. The geometric program is invoked in every iteration of the annealing process to compute the optimal size of each module to give the best packing. The execution time is much faster (at least 15 times faster for data sets with more than 50 modules) than that of the most updated previous work by Murata and Kuh (1998). For a benchmark data with 49 modules, we take 3.7 h in total for the whole annealing process using a 600-MHz Pentium III processor while the convex programming approach described by Murata and Koh needs seven days using a 250-MHz DEC Alpha. Our technique will also be applicable to other floorplanning algorithms that use constraint graphs to find module positions in the final packing.

Thermal conductivities of six oriented semicrystalline polymers which range from 0.37 to 0.63 in crystallinity and 1 to 5 in draw ratio λ (up to about 15 for two polymers) have been measured between 100 and 340 K. It was found that for increasing λ the conductivity K∥ (along the draw direction n̂) increases rapidly while K⊥ (normal to n̂) decreases slightly; K∥ also increases with temperature, but K⊥ shows no simple pattern in temperature dependence. These general features can be reproduced reasonably well at low draw ratio (λ < 5) by the modified Maxwell model, and the discrepancy in details may be attributed to the fact that the model does not take into account the possible anisotropy of the amorphous phase of the oriented polymers. At high draw ratio the intercrystalline bridge effect becomes important, and one must resort to the Takayanagi model, but the lack of corroborating x‐ray data has rendered a detailed comparison impossible.

Abstract. The Hammersley and Halton point sets, two well known low discrepancy sequences, have been used for quasi-Monte Carlo integration in previous research. A deterministic formula generates a uniformly distributed and stochastic-looking sampling pattern, at low computational cost. The Halton point set is also useful for incremental sampling. In this paper, we discuss detailed implementation issues and our experience of choosing suitable bases of the point sets, not just on the 2D plane, but also on a spherical surface. The sampling scheme is also applied to ray tracing, with a significant improvement in error.

The Hammersley and Halton point sets, two well known low discrepancy sequences, have been used for quasi-Monte Carlo integration in previous research. A deterministic formula generates a uniformly distributed and stochastic-looking sampling pattern, at low computational cost. The Halton point set is also useful for incremental sampling. In this paper, we discuss detailed implementation issues and our experience of choosing suitable bases of the point sets, not just on the 2D plane, but also on a spherical surface. The sampling scheme is also applied to ray tracing, with a significant improvement in error.