Related papers: Suggestion for a Fast Heuristic for the Hamiltonia…

This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compares its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of…

We proposed an algorithm that covers some cases of Hamilton Circuit Problem.

We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G. In…

An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying graph. In this note we demonstrate that, for difficult…

We present a memetic algorithm (\maa) approach for finding a Hamiltonian cycle in a Hamiltonian graph. The \ma is based on a proven approach to the Asymmetric Travelling Salesman Problem (\atspp) that, in this contribution, is boosted by…

In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…

We present CertifyHAM, an algorithm which takes as input a graph G and either finds a Hamilton cycle of G or it outputs that such a cycle does not exists. If G=G(n, p) and p >2000/n then the expected running time of CertifyHAM is O(n/p).…

In this pedagogical work we reviewed the mathematical formalism and the physical interpretation, based on statistical mechanics, of the meta-heuristics called simulated annealing. Moreover, we presented the mathematical formulation of the…

This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…

This paper studies the application of the simulated annealing metaheuristic on the identical parallel machine scheduling problem, a variant of the broader optimal job scheduling problem. In the identical parallel machine scheduling problem,…

There are well developed theoretical tools to analyse how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand…

We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.

We devise greedy heuristics tailored for synthesizing quantum circuits that implement a specified set of Pauli rotations. Our heuristics are designed to minimize either the count of entangling gates or the depth of entangling gates, and…

We present an algorithm CRE, which either finds a Hamilton cycle in a graph $G$ or determines that there is no such cycle in the graph. The algorithm's expected running time over input distribution $G\sim G(n,p)$ is $(1+o(1))n/p$, the…

We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…

From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by…

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…

In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard…