English
Related papers

Related papers: 5/4 approximation for Symmetric TSP

200 papers

We present a fast combinatorial $3/4$-approximation algorithm for the maximum asymmetric TSP with weights zero and one. The approximation factor of this algorithm matches the currently best one given by Bl\"aser in 2004 and based on linear…

Data Structures and Algorithms · Computer Science 2014-08-08 Katarzyna Paluch

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

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

M\"omke and Svensson presented a beautiful new approach for the traveling salesman problem on a graph metric (graph-TSP), which yields a $4/3$-approximation guarantee on subcubic graphs as well as a substantial improvement over the…

Data Structures and Algorithms · Computer Science 2020-03-04 Alantha Newman

One of the most studied extensions of the famous Traveling Salesperson Problem (TSP) is the {\sc Multiple TSP}: a set of $m\geq 1$ salespersons collectively traverses a set of $n$ cities by $m$ non-trivial tours, to minimize the total…

Data Structures and Algorithms · Computer Science 2023-07-17 Max Deppert , Matthias Kaul , Matthias Mnich

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 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 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

The cost due to delay in services may be intrinsically different for various applications of vehicle routing such as medical emergencies, logistical operations, and ride-sharing. We study a fundamental generalization of the Traveling…

Data Structures and Algorithms · Computer Science 2022-08-10 Majid Farhadi , Jai Moondra , Prasad Tetali , Alejandro Toriello

The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all $n$ teams is minimized under the…

Data Structures and Algorithms · Computer Science 2023-09-06 Jingyang Zhao , Mingyu Xiao

The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance…

Discrete Mathematics · Computer Science 2014-03-03 Stefan Hougardy , Rasmus T. Schroeder

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.

Computer Science and Game Theory · Computer Science 2015-05-13 Katarzyna Paluch , Marcin Mucha , Aleksander Madry

The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the…

Data Structures and Algorithms · Computer Science 2014-05-09 Arka Bhattacharya

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual,…

Neural and Evolutionary Computing · Computer Science 2023-10-31 Sasan Mahmoudinazlou , Changhyun Kwon

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

The traveling salesman problem (TSP) is a cornerstone of combinatorial optimization and has deeply influenced the development of algorithmic techniques in both exact and approximate settings. Yet, improving on the decades-old bounds for…

Data Structures and Algorithms · Computer Science 2026-04-08 Justin Dallant , László Kozma

In this paper, we study the prize-collecting rural postman problem (PCRPP), a variant of the rural postman problem. Given a PCRPP instance consisting of an undirected graph whose edges have nonnegative lengths and nonnegative profits,…

Data Structures and Algorithms · Computer Science 2026-05-26 Hong Li , Jianping Li , Wei Li , Runtao Xie , Xiaoxiao Yang

A long-standing conjecture for the traveling salesman problem (TSP) states that the integrality gap of the standard linear programming relaxation of the TSP is at most 4/3. Despite significant efforts, the conjecture remains open. We…

Data Structures and Algorithms · Computer Science 2023-07-11 Billy Jin , Nathan Klein , David P. Williamson

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to…

Artificial Intelligence · Computer Science 2020-05-28 Jakob Bossek , Pascal Kerschke , Heike Trautmann

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