Related papers: Suggestion for a Fast Heuristic for the Hamiltonia…
In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
We describe a hybrid procedure for solving the traveling salesman problem (TSP) to provable optimality. We first sparsify the instance, and then use a hybrid algorithm that combines a branch-and-cut TSP solver with a Hamiltonian cycle…
In this paper, we focus on the solution of a hard single machine scheduling problem by new heuristic algorithms embedding techniques from machine learning field and scheduling theory. These heuristics transform an instance of the hard…
A feedback stabilization scheme to stabilize a classical reacting Hamiltonian system is proposed. It is based on transforming a saddle-type equilibrium to an asymptotically stable one, and is given in a simple and algorithmic way. The…
We provide an annotated bibliography for the study of Hamilton cycles in random graphs and hypergraphs.
Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability…
We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it is shown that the input size of the converted instance is a…
In order to find Hamiltonian cycle, algorithm should find edges that creates a Hamiltonian cycle. Higher number of edges creates more possibilities to check to solve the problem. Algorithm rests on analysis of original graph and opposite…
This paper investigated the problem of embedding a simple Hamiltonian Cycle with n vertices on n points inside a simple polygon. This problem seeks to embed a straight-line cycle (without bends), which does not intersect either itself or…
We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian Cycle Problem (HCP) in an undirected graph of order $n$. Although finding a Hamiltonian cycle is not theoretically guaranteed, we have observed that…
As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We design a randomized algorithm that finds a Hamilton cycle in $\mathcal{O}(n)$ time with high probability in a random graph $G_{n,p}$ with edge probability $p\ge C \log n / n$. This closes a gap left open in a seminal paper by Angluin and…
We study the glued-trees problem of Childs et. al. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the…
The state of the art in local search for the Traveling Salesman Problem is dominated by ejection chain methods utilising the Stem-and-Cycle reference structure. Though effective such algorithms employ very little information in their…
In the paper, the new approach to the scheduling problem are described. The approach deals with the problem of planning the cyclic production and proposes to consider such scheduling problem as the cyclic job-shop problem of the order k,…