Related papers: The Relative Exponential Time Complexity of Approx…
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…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Let $\Phi = (V, \mathcal{C})$ be a constraint satisfaction problem on variables $v_1,\dots, v_n$ such that each constraint depends on at most $k$ variables and such that each variable assumes values in an alphabet of size at most $[q]$.…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a…
We study approximation of the embedding $\ell_p^m \hookrightarrow \ell_q^m$, $1 \leq p < q \leq \infty$, based on randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance where $n \ll m$. By…
Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in…
This work studies the problem of constructing a representative workload from a given input analytical query workload where the former serves as an approximation with guarantees of the latter. We discuss our work in the context of workload…
In this paper we focus on problems which do not admit a constant-factor approximation in polynomial time and explore how quickly their approximability improves as the allowed running time is gradually increased from polynomial to…
We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…
This paper shows that the satisfiability problem for probabilistic CTL (PCTL, for short) is undecidable. By a reduction from $1\frac{1}{2}$-player games with PCTL winning objectives, we establish that the PCTL satisfiability problem is…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…