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In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…

Data Structures and Algorithms · Computer Science 2016-01-08 Daniel Marx , Ario Salmasi , Anastasios Sidiropoulos

The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified…

Data Structures and Algorithms · Computer Science 2015-06-02 S. Fekete , S. Khuller , M. Klemmstein , B. Raghavachari , Neal E. Young

We consider the design of sublinear space and query complexity algorithms for estimating the cost of a minimum spanning tree (MST) and the cost of a minimum traveling salesman (TSP) tour in a metric on $n$ points. We first consider the…

Data Structures and Algorithms · Computer Science 2023-05-04 Yu Chen , Sanjeev Khanna , Zihan Tan

We present a $1.5$-approximation for the Metric Path Traveling Salesman Problem (Path TSP). All recent improvements on Path TSP crucially exploit a structural property shown by An, Kleinberg, and Shmoys [Journal of the ACM, 2015], namely…

Discrete Mathematics · Computer Science 2018-10-23 Rico Zenklusen

In this paper, we study the approximability of the metric Traveling Salesman Problem (TSP) and prove new explicit inapproximability bounds for that problem. The best up to now known hardness of approximation bounds were 185/184 for the…

Computational Complexity · Computer Science 2013-06-12 Marek Karpinski , Michael Lampis , Richard Schmied

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

The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph…

Artificial Intelligence · Computer Science 2020-07-10 Amal Nammouchi , Hakim Ghazzai , Yehia Massoud

We consider the problem of designing sublinear time algorithms for estimating the cost of a minimum metric traveling salesman (TSP) tour. Specifically, given access to a $n \times n$ distance matrix $D$ that specifies pairwise distances…

Data Structures and Algorithms · Computer Science 2020-06-11 Yu Chen , Sampath Kannan , Sanjeev Khanna

The $k$-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces $k$ edges of the tour by $k$ other edges, as long as this yields a shorter tour. We…

Data Structures and Algorithms · Computer Science 2023-05-17 Ulrich A. Brodowsky , Stefan Hougardy , Xianghui Zhong

The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…

Emerging Technologies · Computer Science 2013-03-27 Jeff Jones , Andrew Adamatzky

With the aid of the relaxed polygonal inequality (introduced by Fagin et al.) we strive to extend the applicability of Christofides approximation technique to the scope of all complete finite weighted graphs with positive weights. First…

Metric Geometry · Mathematics 2021-05-18 Mateusz Krukowski , Filip Turoboś

In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of $n$ regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present…

Computational Geometry · Computer Science 2012-04-27 Adrian Dumitrescu

We consider the time-dependent traveling salesman problem (TDTSP), a generalization of the asymmetric traveling salesman problem (ATSP) to incorporate time-dependent cost functions. In our model, the costs of an arc can change arbitrarily…

Optimization and Control · Mathematics 2018-05-04 Christoph Hansknecht , Imke Joormann , Sebastian Stiller

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

The Traveling Salesman Problem (TSP) in the $d$-dimensional Euclidean space is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial…

Data Structures and Algorithms · Computer Science 2025-04-07 Tobias Mömke , Hang Zhou

We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…

Data Structures and Algorithms · Computer Science 2022-04-22 Lee-Ad Gottlieb , Robert Krauthgamer , Havana Rika

The Travelling Salesman Problem is one the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides's algorithm with approximation…

Data Structures and Algorithms · Computer Science 2011-10-05 Marcin Mucha

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…

Quantum Physics · Physics 2026-05-18 Alejandro Mata Ali , Iñigo Perez Delgado , Aitor Moreno Fdez. de Leceta

The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed…

Data Structures and Algorithms · Computer Science 2025-09-17 Václav Blažej , Andreas Emil Feldmann , Foivos Fioravantes , Paweł Rzążewski , Ondřej Suchý

The Traveling Salesperson Problem (TSP) is one of the best-known combinatorial optimisation problems. However, many real-world problems are composed of several interacting components. The Traveling Thief Problem (TTP) addresses such…

Neural and Evolutionary Computing · Computer Science 2020-06-08 Jakob Bossek , Aneta Neumann , Frank Neumann