Related papers: The Computational Complexity of the Traveling Sale…
The ATSP polytope can be expressed by asymmetric polynomial size linear program.
Yatsenko gives a polynomial-time algorithm for solving the traveling salesman problem. We examine the correctness of the algorithm and its construction. We also comment on Yatsenko's evaluation of the algorithm.
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…
In this short note, the dual problem for the traveling salesman problem is constructed through the classic Lagrangian. The existence of optimality conditions is expressed as a corresponding inverse problem. A general 4-cities instance is…
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…
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 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 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,…
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…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
We consider the Travelling Salesman Problem with Vertex Requisitions, where for each position of the tour at most two possible vertices are given. It is known that the problem is strongly NP-hard. The proposed algorithm for this problem has…
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…
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…
We introduce the Polychromatic Traveling Salesman Problem (PCTSP), where the input is an edge weighted graph whose vertices are partitioned into $k$ equal-sized color classes, and the goal is to find a minimum-length Hamiltonian cycle that…
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 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…
The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known algorithms in the worst case instances…
The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum…
We consider the NP-hard 2-period balanced travelling salesman problem. In this problem the salesman needs to visit a set of customers in two time periods. A given subset of the customers has to be visited in both periods while the rest of…