Related papers: Complexity of comparing monomials and two improvem…

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…

We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.

This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…

In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

Many Pareto-based multi-objective evolutionary algorithms require to rank the solutions of the population in each iteration according to the dominance principle, what can become a costly operation particularly in the case of dealing with…

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…

We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…

We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting…

We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the…

In this paper we study the complex simultaneous Waring rank for collections of monomials. For general collections we provide a lower bound, whereas for special collections we provide a formula for the simultaneous Waring rank. Our approach…

The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic…

This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…

We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization…

We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in {\sc Singular}, which allow to make a comparison on the basis of…

Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…

We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time…

We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under…