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- Adam Meyerson, Ryan Williams
- PODS
- 2004

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)

- Virginia Vassilevska Williams, Ryan Williams
- 2010 IEEE 51st Annual Symposium on Foundations of…
- 2010

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 > 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)

- Mihai Patrascu, Ryan Williams
- SODA
- 2010

We describe reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems. We show that attaining any of the following bounds would improve the state of the art in algorithms for SAT:
• an <i>O(n<sup>k-ε</sup>)</i> algorithm for <i>k</i>-Dominating Set, for any <i>k</i>… (More)

- Ryan Williams
- Inf. Process. Lett.
- 2009

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)

- Ryan Williams, Carla P. Gomes, Bart Selman
- IJCAI
- 2003

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)

- Ioannis Koutis, Ryan Williams
- ICALP
- 2009

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
- STOC
- 2014

We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two <i>n</i> × <i>n</i> matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense <i>n</i>-node directed graphs with arbitrary edge weights. On the real RAM, where additions and comparisons of reals are unit… (More)

For a pattern graph H on k nodes, we consider the problems of finding and counting the number of (not necessarily induced) copies of H in a given large graph G on n nodes, as well as finding minimum weight copies in both node-weighted and edge-weighted graphs. Our results include: The number of copies of an H with an independent set of size s can be… (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> > 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)

- Ryan Williams
- SIAM J. Comput.
- 2010

The P vs NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We still do not know if even a slight algorithmic improvement over exhaustive search is universally possible for all NP problems, and to date no major consequences have been derived from the assumption that an improvement… (More)