Related papers: Quantum Speedups for Group Relaxations of Integer …
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…
Ising machines (IM) are physics-inspired alternatives to von Neumann architectures for solving hard optimization tasks. By mapping binary variables to coupled Ising spins, IMs can naturally solve unconstrained combinatorial optimization…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Polyhedral compilers can perform complex loop optimizations that improve parallelism and cache behaviour of loops in the input program. These transformations result in significant performance gains on modern processors which have large…
Missing data presents a critical challenge in real-world datasets, significantly degrading the performance of machine learning models. While Large Language Models (LLMs) have recently demonstrated remarkable capabilities in tabular data…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and…
We present an accelerated relax-and-round algorithm for concave coverage problems, which generalize the classic maximum coverage problem. Building on the relax-and-round framework of Barman et al. [STACS 2021], we propose two significant…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of…
In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming (MIP) relaxations.…
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…
A significant hurdle towards realization of practical and scalable quantum computing is to protect the quantum states from inherent noises during the computation. In physical implementation of quantum circuits, a long-distance interaction…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…