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The multivariate moment problem is investigated in the general context of the polynomial algebra $\mathbb{R}[x_i \mid i \in \Omega]$ in an arbitrary number of variables $x_i$, $i\in \Omega$. The results obtained are sharpest when the index…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
In this paper we study the classical single machine scheduling problem where the objective is to minimize the total weight of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or…
One of the driving problems in the CSP area is the Dichotomy Conjecture, formulated in 1993 by Feder and Vardi [STOC'93], stating that for any fixed relational structure G the Constraint Satisfaction Problem CSP(G) is either NP--complete or…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general…
Building upon recent work by the author, we prove that multivariate integration in the following subspace of the Wiener algebra over $[0,1)^d$ is strongly polynomially tractable: \[ F_d:=\left\{ f\in C([0,1)^d)\:\middle| \:…
Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…
This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…
What is the value of input information in solving linear programming? The celebrated ellipsoid algorithm tells us that the full information of input constraints is not necessary; the algorithm works as long as there exists an oracle that,…
We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by…
Problems of segmentation, denoising, registration and 3D reconstruction are often addressed with the graph cut algorithm. However, solving an unconstrained graph cut problem is NP-hard. For tractable optimization, pairwise potentials have…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
The article considers one of the possible generalizations of constraint satisfaction problems where relations are replaced by multivalued membership functions. In this case operations of disjunction and conjunction are replaced by maximum…