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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)…

In Asymmetric A Priori TSP (with independent activation probabilities) we are given an instance of the Asymmetric Traveling Salesman Problem together with an activation probability for each vertex. The task is to compute a tour that…

Data Structures and Algorithms · Computer Science 2025-10-21 Manuel Christalla , Luise Puhlmann , Vera Traub

Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is then measured by adding the length of the tour and the…

Data Structures and Algorithms · Computer Science 2025-01-14 Jannis Blauth , Nathan Klein , Martin Nägele

In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…

Data Structures and Algorithms · Computer Science 2016-01-08 Daniel Marx , Ario Salmasi , Anastasios Sidiropoulos

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…

Robotics · Computer Science 2007-05-23 Ketan Savla , Francesco Bullo , Emilio Frazzoli

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

We consider the Demand Strip Packing problem (DSP), in which we are given a set of jobs, each specified by a processing time and a demand. The task is to schedule all jobs such that they are finished before some deadline $D$ while…

Data Structures and Algorithms · Computer Science 2024-08-19 Franziska Eberle , Felix Hommelsheim , Malin Rau , Stefan Walzer

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Discrete Mathematics · Computer Science 2016-01-06 Jens Vygen

We give a polynomial time, $(1+\epsilon)$-approximation algorithm for the traveling repairman problem (TRP) in the Euclidean plane and on weighted trees. This improves on the known quasi-polynomial time approximation schemes for these…

Data Structures and Algorithms · Computer Science 2014-09-22 René Sitters

We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $\mathbb{R}^d$, for $d\geq 3$) or…

Computational Geometry · Computer Science 2015-11-26 Adrian Dumitrescu , Csaba D. Tóth

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

This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…

Data Structures and Algorithms · Computer Science 2009-09-11 David Eppstein

The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…

Data Structures and Algorithms · Computer Science 2021-04-05 Lucas Porto Maziero , Fábio Luiz Usberti , Celso Cavellucci

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 study the online Traveling Salesman Problem (TSP) on the line augmented with machine-learned predictions. In the classical problem, there is a stream of requests released over time along the real line. The goal is to minimize the…

Data Structures and Algorithms · Computer Science 2022-06-02 Themis Gouleakis , Konstantinos Lakis , Golnoosh Shahkarami

We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Our algorithm achieves an approximation factor of O(f(g)) on graphs…

Data Structures and Algorithms · Computer Science 2013-05-14 Jeff Erickson , Anastasios Sidiropoulos

The $k-$traveling salesman problem ($k$-TSP) seeks a tour of minimal length that visits a subset of $k\leq n$ points. The traveling repairman problem (TRP) seeks a complete tour with minimal latency. This paper provides constant-factor…

Discrete Mathematics · Computer Science 2022-11-22 Moïse Blanchard , Alexandre Jacquillat , Patrick Jaillet

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

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

The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…

Emerging Technologies · Computer Science 2013-03-27 Jeff Jones , Andrew Adamatzky