Gábor Tardos

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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 in adaptive adversary, we show that the power of randomization in on-line algorithms is severely limited! We prove the existence of an efficient “simulation” of randomized on-line 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)
Twenty years ago, Ajtai, Chvátal, Newborn, Szemerédi, and, independently, Leighton discovered that the crossing number of any graph with v vertices and e > 4v edges is at least ce/v, where c > 0 is an absolute constant. This result, known as the ‘Crossing Lemma,’ has found many important applications in discrete and computational geometry. It is tight up to(More)
We examine the computational power of modular counting, where the modulus m is not a prime power, in the setting of polynomials in Boolean variables over Z m . In particular, we say that a polynomial P weakly represents a Boolean function f (both have n variables) if for any inputs x and y in {0,1}n, we have $P(x)\neq P(y)$ whenever $f(x)\neq f(y)$ .(More)