Related papers: Response to Refutation of Aslam's Proof that NP = …
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope…
We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an…
This article finds the answer to the question: for any problem from which a non-deterministic algorithm can be derived which verifies whether an answer is correct or not in polynomial time (complexity class NP), is it possible to create an…
We point out that the computation of true \emph{proof} and \emph{disproof} numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search. The proof requires a…
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
Entity resolution (ER) refers to the problem of matching records in one or more relations that refer to the same real-world entity. While supervised machine learning (ML) approaches achieve the state-of-the-art results, they require a large…
As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…
The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
We prove an NP upper bound on a theory of integer-indexed integer-valued arrays that extends combinatory array logic with an ordering relation on the index set and the ability to express sums of elements. We compare our fragment with seven…
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
This Letter provides necessary and sufficient conditions on the excitation and measurement pattern (EMP) that guarantee identifiability of a dynamical network that has the structure of a loop. The conditions are extremely simple in their…
We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy…
Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in…
An explicit and computable error estimator for the $hp$ version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide $hp$…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…