Related papers: Number partitioning as random energy model
The number partitioning problem is a classic problem of combinatorial optimization in which a set of $n$ numbers is partitioned into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…
Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the configuration space in a hierarchical manner,…
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…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
Similarly to the derivation of the Gibbs-Boltzmann distribution for structureless indistinguishable particles, we consider multi-particle systems some of which are contained (or delimited) inside others (Problem 1), as well as systems of…
The number partitioning problem can be interpreted physically in terms of a thermally isolated non-interacting Bose gas trapped in a one-dimensional harmonic oscillator potential. We exploit this analogy to characterize, by means of a…
The intrinsic excitation energy of fission fragments is dynamically evaluated in terms of the time dependent pairing equations. These equations are corroborated with two conditions. One of them fixes the number of particles and the another…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two…
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…
We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several field of theoretical and…
From the microscopic view, the energy partition between two fission fragments are associated with the splitting of wave functions of an entangled fissioning system, in contrast to most fission models using an explicit statistical partition…
Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…