• Publications
  • Influence
On the complexity of optimal K-anonymity
TLDR
It is proved that two general versions of optimal k-anonymization of relations are NP-hard, including the suppression version which amounts to choosing a minimum number of entries to delete from the relation. Expand
Subcubic Equivalences between Path, Matrix and Triangle Problems
TLDR
Generic equivalences between matrix products over a large class of algebraic structures used in optimization, verifying a matrix product over the same structure, and corresponding triangle detection problems over the structure are shown. Expand
A new algorithm for optimal 2-constraint satisfaction and its implications
  • Ryan Williams
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 8 December 2005
TLDR
A novel method for exactly solving general constraint satisfaction optimization with at most two variables per constraint with the first exponential improvement over the trivial algorithm, which yields connections between the complexity of some (polynomial time) high-dimensional search problems and some NP-hard problems. Expand
Backdoors To Typical Case Complexity
TLDR
This work proposes a new framework for studying the complexity of reasoning and constraint processing methods, which incorporates general structural properties observed in practical problem instances into the formal complexity analysis and introduces a notion of "backdoors", which are small sets of variables that capture the overall combinatorics of the problem instance. Expand
On the possibility of faster SAT algorithms
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 boundsExpand
Finding paths of length k in O*(2k) time
  • Ryan Williams
  • Mathematics, Computer Science
  • Inf. Process. Lett.
  • 18 July 2008
We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2^[email protected]?poly(n)) time. Our method extends a recent O(2^3^k^/^[emailExpand
Faster all-pairs shortest paths via circuit complexity
TLDR
A new randomized method for computing the min-plus product of two n × n matrices is presented, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense n-node directed graphs with arbitrary edge weights. Expand
Non-uniform ACC Circuit Lower Bounds
  • Ryan Williams
  • Mathematics, Computer Science
  • IEEE 26th Annual Conference on Computational…
  • 8 June 2011
TLDR
The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds. Expand
Improving exhaustive search implies superpolynomial lower bounds
TLDR
It is shown that there are natural NP and BPP problems for which minor algorithmic improvements over the trivial deterministic simulation already entail lower bounds such as NEXP is not in P/poly and LOGSPACE is not equal to NP, and unconditional superpolynomial time-space lower bounds for improving on exhaustive search are proved. Expand
Nonuniform ACC Circuit Lower Bounds
TLDR
The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms entail these lower bounds, while the second step requires a strengthening of the author’s prior work. Expand
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