As a consequence of the Subgoal Theorem and the Projection Lemma, we need only consider projection views that are defined in terms of subgoals. Unfortunately, despite these improvements, we show that the optimization problem is still NP-Hard in the number of subgoals and free variables in the input query. Our proof strategy is as follows. First, we prune the space of potential reformulations by...

We prove the following hardness result for a natural promise variant of the classical CNFsatisfiability problem: Given a CNF-formula where each clause has width w and the guarantee that there exists an assignment satisfying at least g = d2 e − 1 literals in each clause, it is NP-hard to find a satisfying assignment to the formula (that sets at least one literal to true in each clause). On the o...

We show that the maximum success probability of players sharing quantum entanglement in a twoplayer game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion NEXP ⊆ MIP∗, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, imp...

Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reeecting the goodness-of-t of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1994) introduced a Bayesian metric, called the BDe metric, that computes the relative posterior...

Given a 3-SAT formula, a graph can be constructed in polynomial time such that the graph is a point visibility graph if and only if the 3-SAT formula is satisfiable. This reduction establishes that the problem of recognition of point visibility graphs is NP-hard.

We consider a special class of art gallery problems inspired by wireless localization. Given a polygonal region P, place and orient guards each of which broadcasts a unique key within a fixed angular range. In contrast to the classical art gallery setting, broadcasts are not blocked by the boundary of P. At any point in the plane one must be able to tell whether or not one is located inside P o...

There exist a number of problem classes for which obtaining the exact solution becomes exponentially expensive with increasing problem size. The quadratic assignment problem (QAP) or the travelling salesman problem (TSP) are just two examples of such NP-hard problems. In practice, approximate algorithms are employed to obtain a suboptimal solution, where one must face a trade-off between comput...

We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the ...

In analogy with NP, a language L is in the class NQP if the strings in L are exactly those accepted by a polynomial-time quantum machine with non-zero probability. Previously, Adleman, Demarrais and Huang showed that NQP PP. The sharper upper bound NQP coC=P is implicit in Adleman et al. and results of Fortnow and Rogers. Here we prove that in fact NQP and coC=P are the same class, by showing t...