Hard Thinking about Hard and Easy Cases in Security Studies

General and Fractional Hypertree Decompositions: Hard and Easy Cases

Hypertree decompositions, as well as the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHD) are hypergraph decomposition methods successfully used for answering conjunctive queries and for the solution of constraint satisfaction problems. Each hypergraph H has a width relative to each of these decomposition methods: its ...

(H, C, K)-Coloring: Fast, Easy, and Hard Cases

We define a variant of the H-coloring problem by fixing the number of preimages of a subset C of the vertices of H, thus allowing parameterization. We provide sufficient conditions to guarantee that the problem can be solved in O(kn+ f(k, H)) steps where f is a function depending only on the number k of fixed preimages and the graph H, and in O(nk+α) steps where α is a constant independent of k...

Easy and Hard Conformant Planning

Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple forms of disjunctive inference. We report an efficient but incomplete planner capable of solving ...

Distinguishing Easy and Hard Instances

Hard cases

Mr R. Gument Q.C.: May it please your Lordship I appear for the plaintiffs, T. Cobley et al. in this action. The facts are straightforward and simply recounted. On or about the 10th of October 2000, the plaintiffs submitted a typescript of a scientific paper to the editors of the journal Nascence. Some two weeks later, they received a communication from the editors stating that their paper woul...