Related papers: A Polyhedral Model for Enumeration and Optimizatio…
Approximate circuit design has gained significance in recent years targeting error tolerant applications. In this paper, we first demonstrate that the commonly used assumption that the inputs to the adder are uniformly distributed results…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
\emph{Reductions} combine collections of input values with an associative (and usually also commutative) operator to produce either a single, or a collection of outputs. They are ubiquitous in computing, especially with big data and deep…
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…
Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes…
In multidisciplinary optimization the designer needs to find solution to optimization problems which include a number of usually contradicting criteria. Such a problem is mathematically related to the field of nonlinear vector optimization…
We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
In this paper, we present a work in progress about a deep learning based approach for automatic code optimization in polyhedral compilers. The proposed technique explores combinations of affine and non-affine loop transformations to find…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex {vector} optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP,…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the…