Related papers: Phase transition in the assignment problem for ran…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
This paper presents stop conditions for solving General Assignment Problems (GAP), in particular for Travel Salesman Problem in an Euclidian 2D space the well known condition Jordan's simple curve and opposite condition for the Knight Tour…
We study the phase transition phenomenon inherent in the shuffled (permuted) regression problem, which has found numerous applications in databases, privacy, data analysis, etc. In this study, we aim to precisely identify the locations of…
In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. (The…
The genetic algorithm includes some parameters that should be adjusted, so as to get reliable results. Choosing a representation of the problem addressed, an initial population, a method of selection, a crossover operator, mutation…
This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling…
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…
The QXORSAT problem is the quantified version of the satisfiability problem XORSAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXORSAT instances. We give a…
We study numerically the maximum $z$-matching problems on ensembles of bipartite random graphs. The $z$-matching problems describes the matching between two types of nodes, users and servers, where each server may serve up to $z$ users at…
In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…
We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such…
In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random…
One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a…
The Assignment problem is a fundamental and well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, a group of agents expresses preferences over a set of items,…
We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.
In this paper discussed procedure of separation of the original problem with several vehicles to a number of simpler problems with one vehicle which based on the matrix approach.
We explore phase transitions of plan modification, which mainly focus on the conformant planning problems. By analyzing features of plan modification in conformant planning problems, quantitative results are obtained. If the number of…
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…
We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
A variant of the well-known Assignment Problem is studied in this paper, where pairs of assignments are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which models real…