We consider the following two questions:
The small-set expansion conjecture introduced by Raghavendra and Steuerer is a natural hardness assumption concerning the problem of approximating edge expansion of small sets (of size $\delta n$) in graphs. It was shown to be intimately connected to the well-known Unique Games Conjecture.
Pursuing this line of research further, we obtain the following results:
Charles Simonyi, Chairman of the Institute’s Board of Trustees and President and CEO of Intentional Software Corporation, is the first and only “space tourist” to fly twice: first in 2007 and most recently in 2009, for a combined total of twenty-eight days in space. In this talk, Dr. Simonyi discusses daily life in a spacecraft and on the International Space Station, and shows footage of the dynamic return trip from orbit to the ground in Kazakhstan.