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It is known that every critical independent set forms a crown.

A graph is König-Egerváry if every maximum independent set is a crown.

We introduce an mixed integer programming formulation of the node partitioning and cycles creation problem, and also heuristic algorithms for solving this problem. Joint work with: Kai Hoppmann, Thorsten Koch and Gioni Mexi (ZIB, Berlin, Germany) Abstract: In the online computing framework the instance arrives in form a request sequence, every request must be served immediately, through a decision, which generates some cost. The goal in this research area is to identify the best strategy, also called online algorithm.

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However there are situations where two algorithms have the same ratio, still in practice one is better than the other.

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.

The goal is to find an algorithm which minimizes this ratio over the worst case instance.

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