University of Cambridge > Talks.cam > Optimization and Incentives Seminar > Algorithmic Barriers from Phase Transitions

Algorithmic Barriers from Phase Transitions

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Elena Yudovina.

This talk is cross-listed from the Probability series, because it should be of interest to this seminar as well.

For many random optimization problems we have by now very sharp estimates of the satisfiable regime. At the same time, though, all known polynomial-time algorithms only find solutions in a very small fraction of that regime. We study this phenomenon by examining how the statistics of the geometry of the set of solutions evolve as constraints are added. We prove in a precise mathematical sense that, for each problem studied, the barrier faced by algorithms corresponds to a phase transition in that problem?s solution-space geometry. Roughly speaking, at some problem-specific critical density, the set of solutions shatters and goes from being a single giant ball to exponentially many, well-separated, tiny pieces. All known polynomial-time algorithms work in the ball regime, but stop as soon as the shattering occurs. Besides giving a geometric view of the solution space of random optimization problems our results establish rigorously a substantial part of the 1-step Replica Symmetry Breaking picture of statistical physics for these problems.

This talk is part of the Optimization and Incentives Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2017 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity