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Randomized Rounding Algorithms in Discrete Optimization and Mathematical Programming

Periodic Report Summary 1 - RRADOMP (Randomized Rounding Algorithms in Discrete Optimization and Mathematical Programming)

The project studied randomized rounding algorithms for discrete optimization and mathematical programming problems.

The results of the project were published in the top conferences and journals in the field. In particular there were two papers published in SIAM Journal of Computing (SICOMP) which is one of the two leading journals in Theoretical Computer Science and two papers published in Operations Research (OR), the most competitive journal in Operations Research. In the paper "Matroid Matching: The Power of Local Search" we established that the local search algorithm provides an arbitrary good precision for the computationally hard problem of finding the minimum size matroid matching, the problem defined by L. Lovasz more than 30 years ago. In another SICOMP paper we studied three-dimensional strip packing problem and designed the best known approximation algorithms using the idea of Harmonic transformation and rounding of item sizes.

The papers in OR were devoted to studies of primal-dual online algorithms for online inventory management problems and studies of dynamic robust policies through properties of convexity and supermodularity.