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The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid…

Quantum Physics · Physics 2025-10-01 Christos Lytrosyngounis , Ioannis Lytrosyngounis

The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient…

Quantum Physics · Physics 2026-05-04 Yuefeng Lin , Chao Zheng , Cong Guo

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 the Bounded Multiple Traveling Salesman Problem (BMTSP), a tour for each salesman, that starts and ends at the depot and that respects the bounds on the number of cities that a feasible salesman tour should satisfy, is to be constructed.…

Discrete Mathematics · Computer Science 2024-05-30 Víctor Pacheco-Valencia , Nodari Vakhania

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

The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We study the traveling salesman problem when the positions of the…

Disordered Systems and Neural Networks · Physics 2019-10-18 Sergio Caracciolo , Andrea Di Gioacchino , Enrico M. Malatesta , Carlo Vanoni

In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal…

Data Structures and Algorithms · Computer Science 2009-09-29 Bodo Manthey , L. Shankar Ram

The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with…

Data Structures and Algorithms · Computer Science 2023-10-12 René van Bevern , Daniel A. Skachkov

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…

Quantum Physics · Physics 2026-05-28 Alessia Ciacco , Luigi Di Puglia Pugliese , Francesca Guerriero

In this paper, we provide a novel strategy for solving Traveling Salesman Problem, which is a famous combinatorial optimization problem studied intensely in the TCS community. In particular, we consider the imitation learning framework,…

Machine Learning · Computer Science 2022-10-13 Pingbang Hu

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 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 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…

Data Structures and Algorithms · Computer Science 2009-09-07 Michel X. Goemans , Nicholas J. A. Harvey , Kamal Jain , Mohit Singh

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution…

Data Structures and Algorithms · Computer Science 2008-12-30 Vladimir Deineko , Alexander Tiskin

The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide…

Computational Geometry · Computer Science 2025-04-16 Benjamin Aram Berendsohn , Hwi Kim , László Kozma

We study integrality gaps and approximability of two closely related problems on directed graphs. Given a set V of n nodes in an underlying asymmetric metric and two specified nodes s and t, both problems ask to find an s-t path visiting…

Data Structures and Algorithms · Computer Science 2010-06-03 Zachary Friggstad , Mohammad R. Salavatipour , Zoya Svitkina

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition…

Optimization and Control · Mathematics 2015-09-22 Xiaolin Tang , Chunhua Yang , Xiaojun Zhou , Weihua Gui

We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…

Data Structures and Algorithms · Computer Science 2015-03-19 Tobias Mömke , Ola Svensson

The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour of $n$ cities that visits each city $c$ a prescribed number $k_c$ of times. Travel costs may be asymmetric, and visiting a city twice in a row may incur a…

Data Structures and Algorithms · Computer Science 2020-04-22 André Berger , László Kozma , Matthias Mnich , Roland Vincze

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