Alantha Newman
A counterexample to Beck's conjecture on the discrepancy of three permutations.
Mon, 04/18/2011 - 15:01 — SomNambulAuthors: Alantha Newman, Aleksandar Nikolov
Subjects: Discrete Mathematics
AbstractGiven three permutations on the integers 1 through n, consider the set system
consisting of each interval in each of the three permutations. Jozsef Beck
conjectured (c. 1987) that the discrepancy of this set system is O(1). We give
a counterexample to this conjecture: for any positive integer n = 3^k, we
exhibit three permutations whose corresponding set system has discrepancy
Omega(log(n)). Our counterexample is based on a simple recursive construction,
and our proof of the discrepancy lower bound is by induction.Limits of Approximation Algorithms: PCPs and Unique Games (DIMACS Tutorial Lecture Notes).
Tue, 02/23/2010 - 16:02 — SomNambulAuthors: Prahladh Harsha, David Pritchard, Moses Charikar, Matthew Andrews, Sanjeev Arora, Subhash Khot, Dana Moshkovitz, Lisa Zhang, Ashkan Aazami, Dev Desai, Igor Gorodezky, Geetha Jagannathan, Alexander S. Kulikov, Darakhshan J. Mir, Alantha Newman, Aleksandar Nikolov, Gwen Spencer
Subjects: Computational Complexity
AbstractThese are the lecture notes for the DIMACS Tutorial "Limits of Approximation
Algorithms: PCPs and Unique Games" held at the DIMACS Center, CoRE Building,
Rutgers University on 20-21 July, 2009. This tutorial was jointly sponsored by
the DIMACS Special Focus on Hardness of Approximation, the DIMACS Special Focus
on Algorithmic Foundations of the Internet, and the Center for Computational
Intractability with support from the National Security Agency and the National
Science Foundation.
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