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In this presentation, we discuss various connections between unions and intersections of maximum (critical) independent sets of graphs, which lead to deeper understanding of crown structures, in general, and König-Egerváry graphs, in particular.

Abstract: The relocation problem is formulated from a municipal redevelopment project in east Boston.

So people came up with a different technique to compare online algorithms directly with each other, rather than through the optimal offline solution. I would do a survey on this technique, and talk about a related personal work: Best-of-two-worlds analysis of online search, with Spyros Angelopoulos and Shendan Jin.

Abstract: We survey a number of integer programming formulations for the pathwidth and for the treewidth problems.

A set is critical if the difference between its size and the size of its neighborhood is maximum.

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Depending on available information, several approaches have been proposed to model this uncertainty.

You would say that algorithm A is better than algorithm B if it has a smaller ratio.

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

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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