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On the power of randomization for job shop scheduling with k -units length tasks

Tobias Mömke (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In the job shop scheduling problem k -units- J m , there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D . The contribution of this paper are the following results; (i) for d = o ( D ) jobs and every fixed k , the makespan of an optimal schedule is at most D + o ( D ) , which extends the result of [3] for k = 1 ; (ii) a randomized on-line approximation algorithm for k -units-...

On the power of randomization for job shop scheduling with k-units length tasks

Tobias Mömke (2008)

RAIRO - Theoretical Informatics and Applications

In the job shop scheduling problem k-units-Jm, there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D. The contribution of this paper are the following results; (i) for d = o ( D ) jobs and every fixed k, the makespan of an optimal schedule is at most D+ o(D), which extends the result of [3] for k=1; (ii) a randomized on-line approximation...

On the queue-size distribution in the multi-server system with bounded capacity and packet dropping

Oleg Tikhonenko, Wojciech M. Kempa (2013)

Kybernetika

A multi-server M / M / n -type queueing system with a bounded total volume and finite queue size is considered. An AQM algorithm with the “accepting” function is being used to control the arrival process of incoming packets. The stationary queue-size distribution and the loss probability are derived. Numerical examples illustrating theoretical results are attached as well.

On the rate of convergence to the neutral attractor of a family of one-dimensional maps

T. Nowicki, M. Sviridenko, G. Świrszcz, S. Winograd (2009)

Fundamenta Mathematicae

For a family of maps f d ( p ) = 1 - ( 1 - p / d ) d , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

On the weak robustness of fuzzy matrices

Ján Plavka (2013)

Kybernetika

A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Wojciech M. Kempa (2014)

Kybernetika

A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of...

On transitive orientations of G-ê

Michael Andresen (2009)

Discussiones Mathematicae Graph Theory

A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.

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