Related papers: Linear Equations with Ordered Data
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
We consider the problem of describing all non-negative integer solutions to a linear congruence in many variables. This question may be reduced to solving the congruence $x_1 + 2x_2 + 3x_3 + ... + (n-1)x_{n-1} \equiv 0 \pmod n$ where values…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
Given a nonempty set $\mathcal{L}$ of linear orders, we say that the linear order $L$ is $\mathcal{L}$-convex embeddable into the linear order $L'$ if it is possible to partition $L$ into convex sets indexed by some element of $\mathcal{L}$…
The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…
Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
Petri nets are a classical model of concurrency widely used and studied in formal verification with many applications in modeling and analyzing hardware and software, data bases, and reactive systems. The reachability problem is central…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…
We give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. This will be the first step to implementing the structural…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…