# On the AND- and OR-Conjectures: Limits to Efficient Preprocessing

 Computer Science/Discrete Mathematics Seminar II Topic: On the AND- and OR-Conjectures: Limits to Efficient Preprocessing Speaker: Andrew Drucker Affiliation: Massachusetts Institute of Technology; Member, School of Mathematics Date: Tuesday, October 16 Time/Room: 10:30am - 12:30pm/S-101 Video Link: https://video.ias.edu/csmd/drucker2012Oct16

One of the major insights of the fixed-parameter tractability’’ (FPT) approach to algorithm design is that, for many NP-hard problems, it is possible to efficiently *shrink* instances which have some underlying simplicity. This preprocessing can be a powerful first step toward solving such instances. At the same time, many other NP-hard problems have resisted efficient preprocessing. The AND-‘’ and OR-conjectures’’ of Bodlaender, Downey, Fellows, and Hermelin (JCSS 2009) gave a unified explanation of the hardness of many such problems. Since their work, one goal has been to provide more standard complexity-theoretic evidence for these conjectures. After introducing the relevant background, I will describe recent progress in this area. Based on the paper New Limits to Classical and Quantum Instance Compression.’’