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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…

Data Structures and Algorithms · Computer Science 2010-03-30 Gregory Gutin , Daniel Karapetyan

The Traveling Salesman Problem (TSP) is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on…

Data Structures and Algorithms · Computer Science 2025-12-02 Jingyang Zhao , Zimo Sheng , Mingyu Xiao

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…

Optimization and Control · Mathematics 2020-05-08 I. M. Ross , R. J. Proulx , M. Karpenko

A well known N P-hard problem called the Generalized Traveling Salesman Problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing…

Artificial Intelligence · Computer Science 2017-08-15 Camelia-M. Pintea , Petrica C. Pop , Camelia Chira

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…

Data Structures and Algorithms · Computer Science 2017-05-22 Vladimir Ejov , Michael Haythorpe , Serguei Rossomakhine

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,…

Data Structures and Algorithms · Computer Science 2020-10-01 Eranda Cela , Vladimir G. Deineko , Gerhard J. Woeginger

In the Travelling Salesman Problem (TSP), we are given a complete graph $K_n$ together with an integer weighting $w$ on the edges of $K_n$, and we are asked to find a Hamilton cycle of $K_n$ of minimum weight. Let $h(w)$ denote the average…

Data Structures and Algorithms · Computer Science 2014-08-05 Gregory Gutin , Viresh Patel

This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in…

Machine Learning · Computer Science 2019-10-15 Chaitanya K. Joshi , Thomas Laurent , Xavier Bresson

Local search is a widely-employed strategy for finding good solutions to Traveling Salesman Problem. We analyze the problem of determining whether the weight of a given cycle can be decreased by a popular $k$-opt move. Earlier work has…

Data Structures and Algorithms · Computer Science 2019-09-04 Édouard Bonnet , Yoichi Iwata , Bart M. P. Jansen , Łukasz Kowalik

We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…

Data Structures and Algorithms · Computer Science 2024-11-05 Ali Çivril

In many real-world routing problems, decision makers must optimise over sparse graphs such as transportation networks with non-metric costs on the edges that do not obey the triangle inequality. Motivated by finding a sufficiently long…

Data Structures and Algorithms · Computer Science 2024-10-15 Patrick O'Hara , M. S. Ramanujan , Theodoros Damoulas

We present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon…

Discrete Mathematics · Computer Science 2019-07-25 Vera Traub , Jens Vygen , Rico Zenklusen

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting…

Robotics · Computer Science 2025-04-24 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods…

Quantum Physics · Physics 2026-01-28 Kapil Goswami , Gagan Anekonda Veereshi , Peter Schmelcher , Rick Mukherjee

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Discrete Mathematics · Computer Science 2016-01-06 Jens Vygen

We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph $G$, if we can find a spanning tree…

Data Structures and Algorithms · Computer Science 2014-07-11 Satoru Iwata , Alantha Newman , R. Ravi

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with…

Optimization and Control · Mathematics 2021-09-30 Ulrich Pferschy , Rostislav Stanek

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based…

Discrete Mathematics · Computer Science 2012-06-18 Jean-Guillaume Fages , Xavier Lorca

With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…

Artificial Intelligence · Computer Science 2017-05-26 Yihui He , Ming Xiang