  In this paper we develop algorithms of finding homogeneous spaces of
semisimple non-compact Lie groups which do not admit compact Clifford-Klein
forms. We propose a computer program which checks if the given homogeneous
space has a non-vanishing cohomological obstruction (found by Tholozan) to
compact Clifford-Klein forms. By a numerical experiment we show that there is a
large class of homogeneous spaces satisfying Tholozan's condition.
