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We define the robustness of a level set homology class of a function $f: {\mathbb X} \to {\mathbb R}$ as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case has ramifications in medical imaging...
We will present some recent results about testing graph properties in sparse graphs and will discuss graph exploration techniques which allow very efficient algorithms for testing graph properties.
We report on the solution of a real-time scheduling problem that arises in the design of software-based operation control of aircraft. A set of tasks has to be distributed on a minimum number of machines and offsets of the tasks have to be computed. The tasks emit jobs periodically starting at their offset and then need to be executed on the machines without any delay. Also, further constraints in...
We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the non-clairvoyant setting where the size of a job is only known when the job finishes. We show an online algorithm WLAPS that is 8α2-competitive...
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