Related papers: The Floyd-Warshall Algorithm, the AP and the TSP, …

We use admissible permutations and a variant of the Floyd-Warshall algorithm to obtain an optimal solution to the Assignment Problem. Using another variant of the F-W algorithm, we obtain an approximate solution to the Traveling Salesman…

We improve proofs in "The Floyd-Warshall Algorithm, the AP and the TSP (III). We also simplify the method for obtaining a good upper bound for an optimal solution.

The celebrated Floyd-Warshall algorithm efficiently computes the all-pairs shortest path, and its simplicity made it a staple in computer science classes. Frequently, students discover a variant of this Floyd-Warshall algorithm by mixing up…

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 clarify the exposition of Phases 2 and 3a in "The Floyd-Warshall Algorithm, the AP and the TSP". We also improve and simplify theorem 3.6 . In line with clarifying the exposition, we change the matrices in examples 3.4 and 3.5 of "The…

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…

We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and…

In this paper, we consider differential approximability of the traveling salesman problem (TSP). We show that TSP is $3/4$-differential approximable, which improves the currently best known bound $3/4 -O(1/n)$ due to Escoffier and Monnot 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,…

Let M be an nXn symetric matrix, n, even, T, an upper bound for T_OPT, an optimal tour, sigma_T, the smaller-valued perfect matching obtained from alternate edges of T expressed as a product of 2-cycles. Applying the modified Floyd-Warshall…

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…

We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and V\'egh. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus…

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.

Starting with M(a), an n X n asymmetric cost matrix, Jonker and Volgenannt transformed it into a 2n X 2n symmetric cost matrix, M(s)where M(s) has unusual properties. One such property is that an optimal tour in M(s) yields an optimal tour…

We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We…

In the maximum traveling salesman problem (Max TSP) we are given a complete undirected graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. We present a fast combinatorial $\frac…

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…

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the…

In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem…

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.