Related papers: The Random Quadratic Assignment Problem
Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue…
Most previous learning-based graph matching algorithms solve the \textit{quadratic assignment problem} (QAP) by dropping one or more of the matching constraints and adopting a relaxed assignment solver to obtain sub-optimal correspondences.…
The distributed optimal synchronization problem with linear quadratic cost is solved in this paper for multi-agent systems with an undirected communication topology. For the first time, the optimal synchronization problem is formulated as a…
The quadratic assignment problem (QAP) is a fundamental NP-hard task that poses significant challenges for both traditional heuristics and modern learning-based solvers. Existing QAP solvers still struggle to achieve consistently…
Quadratic multiple knapsack problem (QMKP) is a combinatorial optimisation problem characterised by multiple weight capacity constraints and a profit function that combines linear and quadratic profits. We study a stochastic variant of this…
An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
This paper presents in detail the originally developed Quadratic Point Estimate Method (QPEM), aimed at efficiently and accurately computing the first four output moments of probabilistic distributions, using 2n^2+1 sample (or sigma)…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life…
A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
Quantum approximate optimization algorithm (QAOA) aims to solve discrete optimization problems by sampling bitstrings using a parameterized quantum circuit. The circuit parameters (angles) are optimized in the way that minimizes the cost…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
We consider the problem of minimizing cost among one-to-one assignments of $n$ jobs onto $n$ machines. The random assignment problem refers to the case when the cost associated with performing jobs on machines are random variables. Aldous…
Research into the development of special-purpose computing architectures designed to solve quadratic unconstrained binary optimization (QUBO) problems has flourished in recent years. It has been demonstrated in the literature that such…
We investigate special cases of the quadratic assignment problem (QAP) where one of the two underlying matrices carries a simple block structure. For the special case where the second underlying matrix is a monotone anti-Monge matrix, we…
The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of…
Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise…
Recent progress in reinforcement learning has led to remarkable performance in a range of applications, but its deployment in high-stakes settings remains quite rare. One reason is a limited understanding of the behavior of reinforcement…