The Isolation Lemma states that when random weights are assigned to the elements of a finite set $E$, then in any given family of subsets of $E$, exactly one set has the minimum weight, with high probability. In this note, we present two proofs for the fact that it is ... more >>>

In a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner of the so-called Maker-Breaker game on a given set system, even when every set has size at most 11. Since then, there has been no improvement on this result. We prove that the game remains ... more >>>

We investigate the number of pairwise comparisons sufficient to sort $n$ elements chosen from a linearly ordered set. This number is shown to be $\log_2(n!) + o(n)$ thus improving over the previously known upper bounds of the form $\log_2(n!) + \Theta(n)$. The new bound is achieved by the proposed group ... more >>>