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Related papers: The 1-1 algorithm for Travelling Salesman Problem

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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

We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Gael Luna , Tyler Summers

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…

Data Structures and Algorithms · Computer Science 2016-03-22 Szymon Dudycz , Jan Marcinkowski , Katarzyna Paluch , Bartosz Rybicki

The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and…

Data Structures and Algorithms · Computer Science 2017-08-08 Mingyu Xiao , Hiroshi Nagamochi

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

The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…

Quantum Physics · Physics 2025-04-25 Bai Xujun , Shang Yun

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

The symmetric circulant TSP is a special case of the traveling salesman problem in which edge costs are symmetric and obey circulant symmetry. Despite the substantial symmetry of the input, remarkably little is known about the symmetric…

Discrete Mathematics · Computer Science 2022-07-22 Samuel C. Gutekunst , Billy Jin , David P. Williamson

The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…

Quantum Physics · Physics 2018-05-29 Karthik Srinivasan , Saipriya Satyajit , Bikash K. Behera , Prasanta K. Panigrahi

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

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

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

Deciding if a graph is a Hamilton graph, also named the Hamilton cycle problem, is important for discrete mathematics and computer science. Due to no characterization to identify Hamilton graphs effectively, there are no tractable…

Discrete Mathematics · Computer Science 2020-11-17 Heping Jiang

We present a new $(\frac32+\frac1{\mathrm{e}})$-approximation algorithm for the Ordered Traveling Salesperson Problem (Ordered TSP). Ordered TSP is a variant of the classical metric Traveling Salesperson Problem (TSP) where a specified…

Data Structures and Algorithms · Computer Science 2024-05-13 Susanne Armbruster , Matthias Mnich , Martin Nägele

The maximum traveling salesman problem (Max~TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. We prove that, in the case when the edge weights are induced by a metric…

Data Structures and Algorithms · Computer Science 2022-01-12 Vladimir Shenmaier

We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic TSP problem: given a set of $n$ points in the plane, compute a shortest…

Data Structures and Algorithms · Computer Science 2016-07-12 Mark de Berg , Kevin Buchin , Bart M. P. Jansen , Gerhard Woeginger

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

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. (The…

Computational Complexity · Computer Science 2014-07-11 Moustapha Diaby

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

The problem of deciding if a Traveling Salesman Problem (TSP) tour is minimal was proved to be coNP-complete by Papadimitriou and Steiglitz. We give an alternative proof based on a polynomial time reduction from 3SAT. Like the original…

Computational Complexity · Computer Science 2014-03-24 Marzio De Biasi