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The Lovász Local Lemma discovered by Erdős and Lovász in 1975 is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. In 1991, József Beck was the first to demonstrate that a constructive variant can be given under certain more restrictive conditions, starting a(More)
We construct binary codes for fingerprinting. Our codes for <i>n</i> users that are <i>&#949;</i>-secure against <i>c</i> pirates have length <i>O(c<sup>2</sup> log(n/&#949;))</i>. This improves the codes proposed by Boneh and Shaw [3] whose length is approximately the square of this length. Our codes are probabilistic. By proving matching lower bounds we(More)
This paper examines the extremal problem of how many 1-entries an n × n 0–1 matrix can have that avoids a certain fixed submatrix P. For any permutation matrix P we prove a linear bound, settling a conjecture of Zoltán Füredi and Péter Hajnal [8]. Due to the work of Martin Klazar [12], this also settles the conjecture of Stanley and Wilf on the number of(More)
Against an adaptive adversary, we show that the power of ran-domization in online algorithms is severely limited! We prove the existence of an efficient " simulation " of randomized online algorithms by deterministic ones, which is best possible in general. The proof of the upper bound is existential. We deal with the issue of computing the efficient(More)