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The Multiple Traveling Salesman Problem (MTSP) extends the traveling salesman problem by assigning multiple salesmen to visit a set of targets from a common depot, with each target visited exactly once while minimizing total tour length. A…

Optimization and Control · Mathematics 2026-04-28 Abhay Singh Bhadoriya , Deepjyoti Deka , Kaarthik Sundar

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck…

Data Structures and Algorithms · Computer Science 2020-12-29 Hyung-Chan An , Robert Kleinberg , David B. Shmoys

The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost Hamilton cycle in an edge-weighted graph, where costs are defined on all pairs of edges contained in the Hamilton cycle. This is a more general version than the…

Discrete Mathematics · Computer Science 2017-09-05 Brad Woods , Abraham Punnen , Tamon Stephen

In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…

Soft Condensed Matter · Physics 2009-10-30 M. Argollo de Menezes , T. J. P. Penna

The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs.…

Data Structures and Algorithms · Computer Science 2015-08-14 Ola Svensson

We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…

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 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 study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…

Data Structures and Algorithms · Computer Science 2015-03-27 Matthias Mnich , Tobias Mömke

A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…

General Mathematics · Mathematics 2025-02-26 Dhananjay P. Mehendale

Travelling Salesman Problem (TSP) is one of the unsolved problems in computer science. TSP is NP Hard. Till now the best approximation ratio found for symmetric TSP is three by two by Christofides Algorithm more than forty years ago. There…

Data Structures and Algorithms · Computer Science 2021-04-27 Alok Chauhan , Madhusudan Verma

Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained…

Neural and Evolutionary Computing · Computer Science 2020-02-05 Jakob Bossek , Katrin Casel , Pascal Kerschke , Frank Neumann

In response to the Amazon Last-Mile Routing Challenge, Team Permission Denied proposes a hierarchical Travelling Salesman Problem (TSP) optimization with a customized cost matrix. The higher level TSP solves for the zone sequence while the…

Optimization and Control · Mathematics 2023-02-07 Xiaotong Guo , Baichuan Mo , Qingyi Wang

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

The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the…

Optimization and Control · Mathematics 2012-03-20 Adam N. Letchford , Saeideh D. Nasiri , Dirk Oliver Theis

We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related {\em maximum path cover} problem, which asks for a collection of vertex disjoint paths that include the maximum number of…

Data Structures and Algorithms · Computer Science 2024-04-30 Soheil Behnezhad , Mohammad Roghani , Aviad Rubinstein , Amin Saberi

Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We…

Computational Geometry · Computer Science 2010-02-03 Mark de Berg , Fred van Nijnatten , René Sitters , Gerhard J. Woeginger , Alexander Wolff

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

We show that the max entropy algorithm can be derandomized (with respect to a particular objective function) to give a deterministic $3/2-\epsilon$ approximation algorithm for metric TSP for some $\epsilon > 10^{-36}$. To obtain our result,…

Data Structures and Algorithms · Computer Science 2022-12-14 Anna R. Karlin , Nathan Klein , Shayan Oveis Gharan

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…

Data Structures and Algorithms · Computer Science 2019-07-23 Samuel C. Gutekunst , David P. Williamson