Discrete Tomography: A New Research Area in Modern OR

by

Gerhard-Wilhelm Weber

Middle East Technical University

Optimization more and more becomes a key technology also for inverse problems of reconstruction, with many applications in science, technology, OR and economy. Among the inverse problems, discrete tomography (DT) is a modern research field which deals with finite objects from VLSI chip design, from medical imaging or practical fields of distribution and allocation.

This presentation focusses on the utilization of modern optimization methods to approximately resolve the NP-hard reconstruction problem of DT. Our new approaches and introductions base on the utilization of any a priori knowledge given and, recently, on interpretations and algorithms coming from coding theory and optimal experimental design. Here, we combine continuous and discrete optimization with exploiting geometrical symmetries (equivariances), in a framework of statistical learning.

We conclude by mentioning about recent applications in VLSI chip design, by an outlook to future research and inviting to collaboration and common future events in EURO and EUROPT.