Related papers: Where the Really Hard Quadratic Assignment Problem…
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however,…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
The Cyclic Antibandwidth Problem (CABP), a variant of the Antibandwidth Problem, is an NP-hard graph labeling problem with numerous applications. Despite significant research efforts, existing state-of-the-art approaches for CABP are…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form $QAP(A,B)$, by showing that the identity permutation is optimal when $A$ and $B$ are respectively a Robinson similarity and…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and…
The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class…
Abductive reasoning (or Abduction, for short) is among the most fundamental AI reasoning methods, with a broad range of applications, including fault diagnosis, belief revision, and automated planning. Unfortunately, Abduction is of high…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Quadratic Unconstrained Binary Optimization (QUBO) problems are NP-hard problems and many real-world problems can be formulated as QUBO. Currently there are no algorithms known that can solve arbitrary instances of NP-hard problems…
We develop a variable depth search heuristic for the quadratic assignment problem. The heuristic is based on sequential changes in assignments analogous to the Lin-Kernighan sequential edge moves for the traveling salesman problem. We treat…
Test-time adaptation (TTA) aims to adapt a model, initially trained on training data, to test data with potential distribution shifts. Most existing TTA methods focus on classification problems. The pronounced success of classification…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
Online resource allocation is a rich and varied field. One of the most well-known problems in this area is online bipartite matching, introduced in 1990 by Karp, Vazirani, and Vazirani [KVV90]. Since then, many variants have been studied,…
Quantum Software Engineering (QSE) is a research area practiced by tech firms. Quantum developers face challenges in optimizing quantum computing and QSE concepts. They use Stack Overflow (SO) to discuss challenges and label posts with…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is…
Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an…