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

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 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

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

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… Expand

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^/^[email… Expand

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

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

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

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