Related papers: Theory and Applications of N-Fold Integer Programm…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in…
This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the…
It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kampen diagrams, which represent groups as quotients of…
Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…
Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are…
We propose a simple O([n^5/\log n]L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov's "Divide-and-Conquer" algorithm [4], where…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different…