Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, March 30, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Ingo Schurr

Height of bottom-antipodal trees

Unique sink orientations of cubes are a common framework to a wide range of optimization problems. A unique sink orientation of a cube is an orientation of the edge graph of a cube, such that every subcube has a unique sink. Problems like LCP, LP, SCQP, SEB can be translated in such orientations, such that the global sink corresponds to the solution of the original problem. Thus we are interested in understanding the complexity of finding the sink in a unique sink orientation.

The simplex algorithm for example finds the sink of a unique sink orientation. Unfortunately as easy as it can be formulated (follow an outgoing edge), it is bad or difficult to analyze (depending on how the edges are chosen). In this talk we will study a memoryless algorithm for finding the sink of a unique sink orientation of cubes closely related to simplex. Our algorithm does not choose one but all outgoing edges. This algorithm is fast on most bad examples for simplex. Its behavior is completely determined by the so called bottom-antipodal tree.

We will construct examples for which this bottom-antipodal tree has exponential height, i.e. the corresponding algorithm performs badly. On the way we will present the basic concepts and tools.

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