In the convergence theory of Padé approximation, one needs to estimate the size of a set on which a suitably normalized polynomial q is small. For example, one needs to estimate the size of the set of r 2 [0; 1] for which max jtj=1 jq (t)j =min jtj=r jq (t)j is not “too large”. We discuss some old and new problems of this type, and the methods used to solve them. 1. Introduction Let f be a func...

We study a generalization of the constraint satisfaction problem (CSP), the periodic constraint satisfaction problem. An input instance of the periodic CSP is a finite set of “generating” constraints over a structured variable set that implicitly specifies a larger, possibly infinite set of constraints; the problem is to decide whether or not the larger set of constraints has a satisfying assig...

A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree based on a model of speciation and duplication where duplications are clustered in duplication episodes. The goal is to minimize the number of such episodes. T...

A polynomial algorithm for solving the ”Hamiltonian circuit” problem is presented in the paper. Computational complexity of the algorithm is equal to O ( n log 2 n ) where n is the cardinality of the observed graph vertex set. Thus the polynomial solvability for NP -complete problems is proved.

Reduced RLT constraints are a special class of Reformulation-Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform r...

The Isomorphism of Polynomials (IP) [28], which is the main concern of this paper, originally corresponds to the problem of recovering the secret key of a C∗ scheme [26]. Besides, the security of various other schemes (signature, authentication [28], traitor tracing [5], . . . ) also depends on the practical hardness of IP. Due to its numerous applications, the Isomorphism of Polynomials is thu...

Methods for the polynomial eigenvalue problem sometimes need to be followed by an iterative refinement process to improve the accuracy of the computed solutions. This can be accomplished by means of a Newton iteration tailored to matrix polynomials. The computational cost of this step is usually higher than the cost of computing the initial approximations, due to the need of solving multiple li...

The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising polynomial time solvability of the problem in two broad situations.

This paper aims at being a guide to understand polynomial transformations and polynomial reductions between NP-complete problems by presenting the methodologies for polynomial reductions/transformations and the differences between reductions and transformations. To this end the article shows examples of polynomial reductions/transformations and the restrictions to reduce/transform between NP-co...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...