相关论文: On "P = NP: Linear Programming Formulation of the …

This article describes counter example prepared in order to prove that linear formulation of TSP problem proposed in [arXiv:0803.4354] is incorrect (it applies also to QAP problem formulation in [arXiv:0802.4307]). Article refers not only…

Using an approach that seems to be patterned after that of Yannakakis, Hofman argues that an NP-complete problem cannot be formulated as a polynomial bounded-sized linear programming problem. He then goes on to propose a "construct" that he…

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…

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 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…

There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial…

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

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,…

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…

The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the…

In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation…

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.

The problem of deciding if a Traveling Salesman Problem (TSP) tour is minimal was proved to be coNP-complete by Papadimitriou and Steiglitz. We give an alternative proof based on a polynomial time reduction from 3SAT. Like the original…

We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is…

The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…

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…

Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. 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…