Max Plus at Work

Heidergott, Bernd; Olsder, Geert Jan; Woude, Jacob van der

doi:10.1515/9781400865239

Cited by 308 publications

(266 citation statements)

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“…The communication graph G(A) and powers of matrix A are closely related as it is shown in the next theorem, whose proof follows using induction on the length k of the path (see [1]). …”

Section: Definition 8 a Path From Node I To Node J Is A Sequence Of Arcsmentioning

confidence: 97%

“…Remark 31 Theorem (23) can be used for computing the eigenvalues of the irreducible matrices {A ii ; i ∈ n}. In addition, the power algorithm (see [1]) results of great help for computing the eigenvector in case it comes from the solution of equation (11). …”

Section: Algorithmmentioning

confidence: 99%

“…In fact, by transforming the reducible regular matrix into a block upper triangular form, called normal form, and considering a very specific recurrent equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The theoretical mathematical foundation exposed in the paper was taken from ( [1] and [2]) incorporating the author's personal style and trying to improve its statements, as well as its proofs, whenever it was possible. The main idea of the algorithm was inspired by ( [2] and the references quoted therein) and up to the author's knowledge, it has not been exploded and completely developed as is done in this paper before.…”

Section: Introductionmentioning

confidence: 99%

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A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra

Konigsberg

2009

2009 Chinese Control and Decision Conference

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In this paper an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is proposed. Given a matrix of finite size, the problem consists in giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrent equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrent equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed.Mathematics Subject Classification: 08C99, 16Y60, 65F15, 05C50, 15A29, 15A33

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“…The communication graph G(A) and powers of matrix A are closely related as it is shown in the next theorem, whose proof follows using induction on the length k of the path (see [1]). …”

Section: Definition 8 a Path From Node I To Node J Is A Sequence Of Arcsmentioning

confidence: 97%

Section: Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra

Konigsberg

2009

2009 Chinese Control and Decision Conference

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“…It has since been shown to have several application areas such as discrete event simulation, dynamic programming, finite dimensional linear algebra, modelling communication networks, operating systems, combinatorial optimization, solving systems of linear equations, biological sequence comparisons and even problems such as crop rotation [4], [8], [9], [11], [13]. In many scientific and computational applications the structure of MPA matrix multiplication is an important aspect.…”

Section: Max-plus Algebramentioning

confidence: 99%

Max-Plus Algebra and Discrete Event Simulation on Parallel Hierarchical Heterogeneous Platforms

Becker

Lastovetsky

2011

Euro-Par 2010 Parallel Processing Workshops

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Abstract. In this paper we explore computing max-plus algebra operations and discrete event simulations on parallel hierarchal heterogeneous platforms. When performing such tasks on heterogeneous platforms parameters such as the total volume of communication and the top-level data partitioning strategy must be carefully taken into account. Choice of the partitioning strategy is shown to greatly affect the overall performance of these applications due to different volumes of inter-partition communication that various strategies impart on these operations. One partitioning strategy in particular is shown to reduce the execution times of these operations more than other, more traditional strategies. The main goal of this paper is to present benefits waiting to be exploited by the use of max-plus algebra operations on these platforms and thus speeding up more complex and quite common computational topic areas such as discrete event simulation.

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“…The resolution of problem 2 is based on the prediction of the earliest desired output. By reason on the lack of place, we cannot give a complete presentation of the preliminary remarks but the reader can easily find more information in [1] and [8]. The presentation of the model of the P-time Event Graph is also omitted: the reader can find the preliminaries and the presentation of the models in [5].…”

Section: Introductionmentioning

confidence: 99%

Trajectory Tracking Control of a Timed Event Graph with Specifications Defined by a P-time Event Graph

Declerck¹,

Guezzi²

2009

Positive Systems

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The aim of this paper is a trajectory tracking control of Timed Event Graphs with specifications defined by a P-time Event Graph. Two problems are solved on a fixed horizon knowing the current state: The optimal control for favorable past evolution; The prediction of the earliest future evolution of the process. These two parts make up an on-line control which is used on a sliding horizon. Completely defined in (max, +) algebra, the proposed approach is a Model Predictive Control using the componentwise order relation.

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Max Plus at Work

Cited by 308 publications

References 0 publications

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra

Max-Plus Algebra and Discrete Event Simulation on Parallel Hierarchical Heterogeneous Platforms

Trajectory Tracking Control of a Timed Event Graph with Specifications Defined by a P-time Event Graph

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