614,368 research outputs found
Stability of Mine Car Motion in Curves of Invariable and Variable Radii
We discuss our experiences adapting three recent algorithms for maximum common (connected) subgraph problems to exploit multi-core parallelism. These algorithms do not easily lend themselves to parallel search, as the search trees are extremely irregular, making balanced work distribution hard, and runtimes are very sensitive to value-ordering heuristic behaviour. Nonetheless, our results show that each algorithm can be parallelised successfully, with the threaded algorithms we create being clearly better than the sequential ones. We then look in more detail at the results, and discuss how speedups should be measured for this kind of algorithm. Because of the difficulty in quantifying an average speedup when so-called anomalous speedups (superlinear and sublinear) are common, we propose a new measure called aggregate speedup
On the computation of geometric features of spectra of linear operators on Hilbert spaces
Computing spectra is a central problem in computational mathematics with an
abundance of applications throughout the sciences. However, in many
applications gaining an approximation of the spectrum is not enough. Often it
is vital to determine geometric features of spectra such as Lebesgue measure,
capacity or fractal dimensions, different types of spectral radii and numerical
ranges, or to detect essential spectral gaps and the corresponding failure of
the finite section method. Despite new results on computing spectra and the
substantial interest in these geometric problems, there remain no general
methods able to compute such geometric features of spectra of
infinite-dimensional operators. We provide the first algorithms for the
computation of many of these longstanding problems (including the above). As
demonstrated with computational examples, the new algorithms yield a library of
new methods. Recent progress in computational spectral problems in infinite
dimensions has led to the Solvability Complexity Index (SCI) hierarchy, which
classifies the difficulty of computational problems. These results reveal that
infinite-dimensional spectral problems yield an intricate infinite
classification theory determining which spectral problems can be solved and
with which type of algorithm. This is very much related to S. Smale's
comprehensive program on the foundations of computational mathematics initiated
in the 1980s. We classify the computation of geometric features of spectra in
the SCI hierarchy, allowing us to precisely determine the boundaries of what
computers can achieve and prove that our algorithms are optimal. We also
provide a new universal technique for establishing lower bounds in the SCI
hierarchy, which both greatly simplifies previous SCI arguments and allows new,
formerly unattainable, classifications
Linear Combinations of Heuristics for Examination Timetabling
Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset
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