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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

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

In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to…

Data Structures and Algorithms · Computer Science 2022-11-02 Evripidis Bampis , Bruno Escoffier , Niklas Hahn , Michalis Xefteris

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…

Artificial Intelligence · Computer Science 2024-04-18 Bowen Fang , Xu Chen , Xuan Di

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 Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…

Machine Learning · Computer Science 2020-11-04 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

This paper explores a variation of the Traveling Salesperson Problem, where the agent places a circular obstacle next to each node once it visits it. Referred to as the Traveling Salesperson Problem with Circle Placement (TSP-CP), the aim…

Robotics · Computer Science 2024-10-16 David Woller , Masoumeh Mansouri , Miroslav Kulich

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 traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application…

Data Structures and Algorithms · Computer Science 2025-11-10 Sophia Saller , Jana Koehler , Andreas Karrenbauer

The Colored Points Traveling Salesman Problem (Colored Points TSP) is introduced in this work as a novel variation of the traditional Traveling Salesman Problem (TSP) in which the set of points is partitioned into multiple classes, each of…

Computational Geometry · Computer Science 2024-01-09 Saeed Asaeedi

We study a new version of the Traveling Salesperson Problem, called \VectorTSP, where the traveler is subject to discrete acceleration constraints, as defined in the paper-and-pencil game Racetrack (also known as Vector Racer). In this…

Data Structures and Algorithms · Computer Science 2025-02-12 Arnaud Casteigts , Mathieu Raffinot , Mikhail Raskin , Jason Schoeters

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 the Traveling Salesman Problem (TSP), a list of cities and the distances between them are given. The goal is to find the shortest possible route that visits each city exactly once and returns to the original city. The TSP has a wide…

Optimization and Control · Mathematics 2019-06-17 Johnny Seay , Edwin Gonzalez , Stephen Lowe , Jesse Crawford , Bryant Wyatt

Many real-world scenarios involve solving bi-level optimization problems in which there is an outer discrete optimization problem, and an inner problem involving expensive or black-box computation. This arises in space-time dependent…

Optimization and Control · Mathematics 2024-07-12 Isaac Rudich , Quentin Cappart , Manuel López-Ibáñez , Michael Römer , Louis-Martin Rousseau

We study the Online Traveling Salesperson Problem (OLTSP) with predictions. In OLTSP, a sequence of initially unknown requests arrive over time at points (locations) of a metric space. The goal is, starting from a particular point of the…

Data Structures and Algorithms · Computer Science 2023-05-04 Evripidis Bampis , Bruno Escoffier , Themis Gouleakis , Niklas Hahn , Kostas Lakis , Golnoosh Shahkarami , Michalis Xefteris

The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…

Data Structures and Algorithms · Computer Science 2026-04-22 Jan Eube , Kelin Luo , Aneta Neumann , Frank Neumann , Heiko Röglin

We initiate the study of online routing problems with predictions, inspired by recent exciting results in the area of learning-augmented algorithms. A learning-augmented online algorithm which incorporates predictions in a black-box manner…

Data Structures and Algorithms · Computer Science 2022-07-01 Hsiao-Yu Hu , Hao-Ting Wei , Meng-Hsi Li , Kai-Min Chung , Chung-Shou Liao

In this paper we consider the Recoverable Traveling Salesman Problem (TSP). Here the task is to find two tours simultaneously, such that the intersection between the tours is at least a given minimum size, while the sum of travel distances…

Data Structures and Algorithms · Computer Science 2021-11-19 Marc Goerigk , Stefan Lendl , Lasse Wulf

We introduce the $L_p$ Traveling Salesman Problem ($L_p$-TSP), given by an origin, a set of destinations, and underlying distances. The objective is to schedule a destination visit sequence for a traveler of unit speed to minimize the…

Data Structures and Algorithms · Computer Science 2021-07-23 Majid Farhadi , Alejandro Toriello , Prasad Tetali

The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify…

Artificial Intelligence · Computer Science 2023-03-01 Majid Namazi , Conrad Sanderson , M. A. Hakim Newton , Abdul Sattar
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