Related papers: Analysis and Counterexamples Regarding Yatsenko's …
The ATSP polytope can be expressed by asymmetric polynomial size linear program.
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.
This paper describes TSP exact solution of polynomial complexity. It is considered properties of proposed method. Effectiveness of proposed solution is illustrated by outcomes of computer modeling.
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…
In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…
We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
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…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
The aim of the paper is to compare different approximation algorithms for the travelling salesperson problem. We pick the most popular and widespread methods known in the literature and contrast them with a novel approach (the polygonal…
For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…
The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of $\mathbb{R}^N$ is contained on a curve of finite length. We show that for finite sets, the algorithm constructed by Schul (2007)and…
We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses…
Proposed initially from a practical circumstance, the traveling salesman problem caught the attention of numerous economists, computer scientists, and mathematicians. These theorists were instead intrigued by seeking a systemic way to find…
This article presents counter examples for three articles claiming that P=NP. Articles for which it applies are: Moustapha Diaby "P = NP: Linear programming formulation of the traveling salesman problem" and "Equality of complexity classes…
Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the…
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…
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,…