Vol. 21 · No. 5

The paper describes a concept of induced rational parametrisation for curves. Parametrisations of curves are defined in terms of rational parametrisations of simpler or `primitive' curves. The technique has applications in computer graphics and geometric modeling. A range of examples is given.

The primary purpose of parallel computation is the fast execution of computational tasks that require an inordinate amount of time to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. The thesis of this paper is that a second equally important motivation for using parallel computers exists. Specifically, the following question is posed: Can parallel computers, thanks to their multiple processors, do more than simply speed up the solution to a problem? We show that within the paradigm of real-time computation, some classes of problems have the property that a solution to a problem in the class, when computed in parallel, is far superior in quality than the best one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, `better' means `closer to optimal' for optimization problems, `more secure' for cryptographic problems, and `more accurate' for numerical problems. Examples from these classes are presented. In each case, the solution obtained in parallel is significantly, provably, and consistently better than a sequential one. It is important to note that the purpose of this paper is not to demonstrate merely that a parallel computer can obtain a better solution to a computational problem than one derived sequentially. The latter is an interesting (and often surprising) observation in its own right, but we wish to go further. It is shown here that the improvement in quality can be arbitrarily high (and certainly superlinear in the number of processors used by the parallel computer). This result is akin to superlinear speedup — a phenomenon itself originally thought to be impossible.

This paper presents a new approach to on-line fault tolerance via reconfiguration for the systems mapped onto field programmable gate arrays (FPGAs). The fault detection, based on self-checking technique, is introduced at application level; therefore our approach can detect the faults of configurable logic blocks (CLBs) and routing interconnections in the FPGAs concurrently with the normal system work. A grid of tiles is projected on the FPGA structure and a certain number of spare CLBs is reserved inside every tile. The number of spare CLBs per tile, which will be used as a backup upon detecting any faulty CLB, is estimated in accordance with the probability of failure. After locating the faulty CLBs, the faulty tile will be reconfigured with avoiding the faulty CLBs. Our proposed approach uses a combination of hardware and software redundancy. We assume that a module external to the FPGA controls automatically the reconfiguration process in addition to the diagnosis process (DIRC); typically this is an embedded microprocessor having some storage for the various tile configurations. We have implemented our approach using Xilinx Virtex FPGA. The DIRC code is written in JBits software tools. In response to a component failure this approach capitalizes on the unique reconfiguration capabilities of FPGAs and replaces the affected tile with a functionally equivalent one that does not rely on the faulty component. Unlike fixed structure fault-tolerance techniques for ASICs and microprocessors, this approach allows a single physical component to provide redundant backup for several types of components.

The main goal of this research was to investigate the means of intelligent support for retrieval of web documents. We have proposed the architecture of the web tool system — Trillian, which discovers the interests of users without their interaction and uses them for autonomous searching of related web content. Discovered pages are suggested to the user. The discovery of user interests is based on analysis of documents visited by the users previously. We have created a module for completely transparent tracking of the user's movement on the web, which logs both visited URLs and contents of web pages. The post analysis step is based on a variant of the suffix tree clustering algorithm. We primarily focus on overall Trillian architecture design and the process of discovering topics of interests. We have implemented an experimental prototype of Trillian and evaluated the quality, speed and usefulness of the proposed system. We have shown that clustering is a feasible technique for extraction of interests from web documents. We consider the proposed architecture to be quite promising and suitable for future extensions.