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A constructive proof of the general lovász local lemma

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… Expand

Optimal probabilistic fingerprint codes

- G. Tardos
- Computer Science, Mathematics
- STOC '03
- 9 June 2003

We construct binary codes for fingerprinting. Our codes for n users that are ε-secure against c pirates have length O(c2 log(n/ε)). This improves the codes proposed by Boneh and Shaw [3] whose length… Expand

Excluded permutation matrices and the Stanley-Wilf conjecture

- Adam Marcus, G. Tardos
- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 1 July 2004

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… Expand

Optimal probabilistic fingerprint codes

- G. Tardos
- Computer Science, Mathematics
- JACM
- 1 May 2008

We construct binary codes for fingerprinting digital documents. Our codes for n users that are ε-secure against c pirates have length O(c2log(n/ε)). This improves the codes proposed by Boneh and Shaw… Expand

Forbidden paths and cycles in ordered graphs and matrices

At most how many edges can an ordered graph ofn vertices have if it does not contain a fixed forbidden ordered subgraphH? It is not hard to give an asymptotically tight answer to this question,… Expand

Conflict-Free Colourings of Graphs and Hypergraphs

A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of ‘unique’ colour that does not get repeated in E. The smallest number of colours… Expand

Tight bounds for Lp samplers, finding duplicates in streams, and related problems

- H. Jowhari, M. Saglam, G. Tardos
- Computer Science, Mathematics
- PODS
- 21 December 2010

In this paper, we present near-optimal space bounds for <i>L<sub>p</sub></i>-samplers. Given a stream of updates (additions and subtraction) to the coordinates of an underlying vector <i>x</i> in… Expand

High rate fingerprinting codes and the fingerprinting capacity

Including a unique code in each copy of a distributed document is an effective way of fighting intellectual piracy. Codes designed for this purpose that are secure against collusion attacks are… Expand

Local Chromatic Number, KY Fan's Theorem, And Circular Colorings

- G. Simonyi, G. Tardos
- Mathematics, Computer Science
- Comb.
- 6 July 2004

The local chromatic number of a graph was introduced in [14]. It is in between the chromatic and fractional chromatic numbers. This motivates the study of the local chromatic number of graphs for… Expand