Related papers: Limits of Preprocessing

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…

We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…

Finding optimal parameter configurations for tunable GPU kernels is a non-trivial exercise for large search spaces, even when automated. This poses an optimization task on a non-convex search space, using an expensive to evaluate function…

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…

We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget…

We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…

One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…

The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$. We give polynomial-time multiplicative approximation algorithms for…

While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…

The general intractability of the constraint satisfaction problem has motivated the study of restrictions on this problem that permit polynomial-time solvability. One major line of work has focused on structural restrictions, which arise…

Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…

There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…

Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of…

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

Pruning and quantization techniques have been broadly successful in reducing the number of parameters needed for large neural networks, yet theoretical justification for their empirical success falls short. We consider a randomized greedy…