approximation bounds

Optimal Control of Semilinear Graphon Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more

    Scheduling on uniform nonsimultaneous parallel machines

  • Donald K. Friesen
  • Liliana Grigoriu
    • Categories Approximation Algorithms, Combinatorial Optimization, Scheduling Tags ,

    We consider the problem of scheduling on uniform processors with nonsimultaneous machine available times with the purpose of mini\-mi\-zing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within $1.382$ times the optimal maximum completion times. This results from properties of the Multifit algorithm when used for … Read more