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Evaluating the Kernighan-Lin heuristic for hardware/software partitioning

Zoltán Mann, András Orbán, Viktor Farkas (2007)

International Journal of Applied Mathematics and Computer Science

In recent years, several heuristics have been proposed for the hardware/software partitioning problem. One of the most promising directions is the adaptation of the Kernighan-Lin algorithm. The Kernighan-Lin heuristic was originally developed for circuit partitioning, but it has been adapted to other domains as well. Moreover, numerous improvements have been suggested so that now several variants of the original algorithm exist. The aim of this paper is to systematically evaluate the possibilities...

Event-Based Proof of the Mutual Exclusion Property of Peterson’s Algorithm

Ievgen Ivanov, Mykola Nikitchenko, Uri Abraham (2015)

Formalized Mathematics

Proving properties of distributed algorithms is still a highly challenging problem and various approaches that have been proposed to tackle it [1] can be roughly divided into state-based and event-based proofs. Informally speaking, state-based approaches define the behavior of a distributed algorithm as a set of sequences of memory states during its executions, while event-based approaches treat the behaviors by means of events which are produced by the executions of an algorithm. Of course, combined...

Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case

Krzysztof Dębicki, Grzegorz Sikora (2011)

Applicationes Mathematicae

Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of ℙ ( s u p t ∈ [ 0 , T ] ( ∑ i = 1 n λ i B H i ( t ) - c t ) > u ) , where B H i ( t ) : t ≥ 0 , i = 1,...,n, are independent fractional Brownian motions with Hurst parameters H i ∈ ( 0 , 1 ] and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of m i n i = 1 , . . . , n H i .

Finite-volume level set method and its adaptive version in completing subjective contours

Zuzana Krivá (2007)

Kybernetika

In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly...

Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

Qixun Lan, Huawei Niu, Yamei Liu, Huafeng Xu (2017)

Kybernetika

In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving...

Graph fibrations, graph isomorphism, and PageRank

Paolo Boldi, Violetta Lonati, Massimo Santini, Sebastiano Vigna (2006)

RAIRO - Theoretical Informatics and Applications

PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...

Guessing secrets.

Chung, Fan, Graham, Ronald, Leighton, Tom (2001)

The Electronic Journal of Combinatorics [electronic only]

Hierarchical residue number systems with small moduli and simple converters

Tadeusz Tomczak (2011)

International Journal of Applied Mathematics and Computer Science

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k-1, 2k, 2k+1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the...

How to eliminate non-positive circuits in periodic scheduling: a proactive strategy based on shortest path equations

Sid-Ahmed-Ali Touati, Sébastien Briais, Karine Deschinkel (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Usual periodic scheduling problems deal with precedence constraints having non-negative latencies. This seems a natural way for modelling scheduling problems, since task delays are generally non-negative quantities. However, in some cases, we need to consider edges latencies that do not only model task latencies, but model other precedence constraints. For instance in register optimisation problems devoted to optimising compilation, a generic machine or processor model can allow considering access...

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested....

Is GPU the future of Scientific Computing ?

Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Perignon, Christophe Picard, Florian De Vuyst, Christophe Labourdette (2013)

Annales mathématiques Blaise Pascal

These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay),...

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