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1

Exact approaches to late work scheduling on unrelated machines

Liu Xinbo, Wang Wen, Chen Xin, Sterna Malgorzata, Blazewicz Jacek

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 2

285--295

EN

We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments.

2

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

Freihold M., Hofer E. P.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 3

485-499

EN

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically eaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.

3

Sekwencjonowanie DNA z błędami negatywnymi oraz informacją o powtórzeniach

Kwarciak K., Radom M., Formanowicz P.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2008

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z. 151

215-222

PL

W pracy przedstawiony jest algorytm typu podziału i ograniczeń dla problemu sekwencjonowania przez hybrydyzację z błędami negatywnymi oraz częściową informacją o powtórzeniach. Uwzględnienie tego rodzaju informacji możliwe jest ze względu na rozwój technologii stosowanej w eksperymencie hybrydyzacyjnym. Prowadzi ono do rozszerzenia standardowej wersji metody sekwencjonowania przez hybrydyzację oraz do polepszenia jakości uzyskiwanych rozwiązań.

EN

In this paper a branch and bound algorithm for sequencing by hybridization problem with negative errors and partial information about repetitions is presented. Taking into account information of this type is possible because of the development of the technology used in the hybridization experiment. It leads to an extension of the standard sequencing by hybridization method and to an improvement of the quality of the obtained results.