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It is required to find a feasible partitioning which minimizes the number of such cycles.

Problems of this kind are typical in numerous applications, where services are repeatedly provided for a set of customers.

the performance of an online algorithm is compared with the optimal offline solution.

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A graph is König-Egerváry if every maximum independent set is a crown.Some others are just curious and interesting fruits of mathematical imagination.Abstract: While the problem of scheduling unit-time jobs with release dates and deadlines on parallel machines is polynomially solvable via a reduction to the assignment problem, the no-idle requirement destroys this reduction and makes the problem challenging.The attempts to find good formulations for the problems span the period of 15 years, yet without any true success.Nevertheless, some formulations provide potentially useful frameworks for attacking these notorious problems.

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