Related papers: A quantum speedup algorithm for TSP based on quant…
The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known algorithms in the worst case instances…
In the Travelling Salesman Problem (TSP), we are given a complete graph $K_n$ together with an integer weighting $w$ on the edges of $K_n$, and we are asked to find a Hamilton cycle of $K_n$ of minimum weight. Let $h(w)$ denote the average…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
We study the online Traveling Salesman Problem (TSP) on the line augmented with machine-learned predictions. In the classical problem, there is a stream of requests released over time along the real line. The goal is to minimize the…
The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…
Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…
Solving the Traveling Salesperson Problem (TSP) remains a persistent challenge, despite its fundamental role in numerous generalized applications in modern contexts. Heuristic solvers address the demand for finding high-quality solutions…