approximation bounds

Optimal Control of Semilinear Graphon Systems

Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

We investigate optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. A graphon represents a limit object of a converging graph sequence and serves as a generalization of a finite graph, enabling a systematic analysis of large-scale networks. We analyze semilinear graphon dynamical systems and establish state convergence along … Read more

Scheduling on uniform nonsimultaneous parallel machines

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