Ryan Williams

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The technique of <i>k-anonymization</i> has been proposed in the literature as an alternative way to release public information, while ensuring both data privacy and data integrity. We prove that two general versions of optimal <i>k-</i>anonymization of relations are <i>NP-</i>hard, including the suppression version which amounts to choosing a minimum(More)
We say an algorithm on n by n matrices with entries in [-M, M] (or n-node graphs with edge weights from [-M, M]) is truly sub cubic if it runs in O(n^{3-\delta} \poly(\log M)) time for some \delta &#x003E; 0. We define a notion of sub cubic reducibility, and show that many important problems on graphs and matrices solvable in O(n^3) time are equivalent(More)
The k-path problem is to determine if a given graph contains a simple path of length at least k, and if so, produce such a path. When k is given as a part of the input, the problem is wellknown to be NP-complete. The general problem has many practical applications (cf. [3, 15]). The trivial algorithm enumerating all possible k-paths in an n-node graph uses(More)
There has been significant recent progress in reasoning and constraint processing methods. In areas such as planning and finite model-checking, current solution techniques can handle combinatorial problems with up to a million variables and five million constraints. The good scaling behavior of these methods appears to defy what one would expect based on a(More)
The fastest known randomized algorithms for several parameterized problems use reductions to the <i>k</i>-M<scp>l</scp>D problem: detection of multilinear monomials of degree <i>k</i> in polynomials presented as circuits. The fastest known algorithm for <i>k</i>-M<scp>l</scp>D is based on 2<sup><i>k</i></sup> evaluations of the circuit over a suitable(More)
  • Ryan Williams
  • 2011 IEEE 26th Annual Conference on Computational…
  • 2011
The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MOD<sub>m</sub> gates, where <i>m</i> &gt; 1 is an arbitrary constant. We prove the following. ---NEXP, the class of languages accepted in nondeterministic exponential time, does not have nonuniform ACC circuits of polynomial size. The size lower bound(More)