Related papers: A linear time algorithm for the orbit problem over…
In the paper the foundation of the $k$-orbit theory is developed. The theory opens a new simple way to the investigation of groups and multidimensional symmetries. The relations between combinatorial symmetry properties of a $k$-orbit and…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
In this paper, a polynomial time algorithm for finding the set of all cyclic subsets in a graph is presented. The concept of cyclic subsets has already been introduced in an earlier paper. The algorithm finds cyclic subsets in a graph G by…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
We show that the two problems of computing the permanent of an $n\times n$ matrix of $\operatorname{poly}(n)$-bit integers and counting the number of Hamiltonian cycles in a directed $n$-vertex multigraph with…
We study the algorithmic complexity of the problem of deciding whether a Linear Time Invariant dynamical system with rational coefficients has bounded trajectories. Despite its ubiquitous and elementary nature in Systems and Control, it…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization…
This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is…
The complexity of the equation solvability problem is known for nilpotent groups, for not solvable groups and for some semidirect products of Abelian groups. We provide a new polynomial time algorithm for deciding the equation solvability…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
We consider the following problem closely related to graph isomorphism. In a simplified version, the task is to compute the automorphism group of a given set family (or a hypergraph), that is, the group of all automorphisms of the given…
An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…