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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,…

Computational Complexity · Computer Science 2016-09-09 Yair Bartal , Lee-Ad Gottlieb , Robert Krauthgamer

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 study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…

Data Structures and Algorithms · Computer Science 2011-07-07 Sylvia Boyd , René Sitters , Suzanne van der Ster , Leen Stougie

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of…

Machine Learning · Computer Science 2018-11-19 Marcelo O. R. Prates , Pedro H. C. Avelar , Henrique Lemos , Luis Lamb , Moshe Vardi

The Traveling Tournament Problem is a sports-scheduling problem where the goal is to minimize the total travel distance of teams playing a double round-robin tournament. The constraint 'k' is an imposed upper bound on the number of…

Computational Complexity · Computer Science 2021-10-07 Diptendu Chatterjee

We introduce a new bounding approach called Continuity* C*, which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning…

Robotics · Computer Science 2024-12-04 Allen George Philip , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…

Robotics · Computer Science 2023-02-02 Aviv Adler , Oren Gal , Sertac Karaman

This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformulations that approximate the Euclidean distances and…

Artificial Intelligence · Computer Science 2025-07-08 Hiba Bederina

The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…

Optimization and Control · Mathematics 2026-03-30 Steffen Borgwardt , Zachary Sorenson

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…

Quantum Physics · Physics 2007-05-23 Debabrata Goswami , Harish Karnick , Prateek Jain , Hemanta K. Maji

In the bipartite travelling salesman problem (BTSP), we are given $n=2k$ cities along with an $n\times n$ distance matrix and a partition of the cities into $k$ red and $k$ blue cities. The task is to find a shortest tour which alternately…

Optimization and Control · Mathematics 2023-02-13 Vladimir G. Deineko , Bettina Klinz , Gerhard J. Woeginger

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…

Data Structures and Algorithms · Computer Science 2020-09-17 Ola Svensson , Jakub Tarnawski , László A. Végh

Hybrid quantum-classical algorithms can help mitigating the physical limitations of current quantum devices, particularly the low qubit count and the reduced topological connectivity. In this paper, we propose a hybrid technique to solve a…

Quantum Physics · Physics 2026-05-12 Siwei Hu , Victor Lopata , Salvatore Sinno , Shruthi Thuravakkath , Paolo Zuliani

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added…

Quantum Physics · Physics 2025-10-30 Alessia Ciacco , Francesca Guerriero , Eneko Osaba

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

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…

Neural and Evolutionary Computing · Computer Science 2014-01-10 Dogan Corus , Per Kristian Lehre , Frank Neumann , Mojgan Pourhassan

Among the most important variants of the traveling salesman problem (TSP) are those relaxing the constraint that every locus should necessarily get visited, rather taking into account a revenue (prize) for visiting customers. In the…

Optimization and Control · Mathematics 2022-04-18 Enrico Angelelli , Renata Mansini , Romeo Rizzi

In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…

Disordered Systems and Neural Networks · Physics 2018-08-28 Sergio Caracciolo , Andrea Di Gioacchino , Enrico M. Malatesta

We give unconditional parameterized complexity lower bounds on pure dynamic programming algorithms - as modeled by tropical circuits - for connectivity problems such as the Traveling Salesperson Problem. Our lower bounds are higher than the…

Computational Complexity · Computer Science 2025-12-30 Kacper Kluk , Jesper Nederlof