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Related papers: Improved FPT Approximation for Non-metric TSP

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We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…

Discrete Mathematics · Computer Science 2012-09-18 András Sebő , Jens Vygen

In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…

Data Structures and Algorithms · Computer Science 2020-10-01 Eranda Cela , Vladimir G. Deineko , Gerhard J. Woeginger

Given a set $\cal P$ of points in the Euclidean plane and two triangulations of $\cal P$, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other.…

Data Structures and Algorithms · Computer Science 2019-10-15 Qilong Feng , Shaohua Li , Xiangzhong Meng , Jianxin Wang

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

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

The Metric $k$-median problem over a metric space $(\mathcal{X}, d)$ is defined as follows: given a set $L \subseteq \mathcal{X}$ of facility locations and a set $C \subseteq \mathcal{X}$ of clients, open a set $F \subseteq L$ of $k$…

Data Structures and Algorithms · Computer Science 2020-07-24 Dishant Goyal , Ragesh Jaiswal , Amit Kumar

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of $m$ salesmen jointly visit all cities from a set of $n$ cities. The mTSP models many important real-life…

Discrete Mathematics · Computer Science 2022-01-07 Kristóf Bérczi , Matthias Mnich , Roland Vincze

In the Bounded Multiple Traveling Salesman Problem (BMTSP), a tour for each salesman, that starts and ends at the depot and that respects the bounds on the number of cities that a feasible salesman tour should satisfy, is to be constructed.…

Discrete Mathematics · Computer Science 2024-05-30 Víctor Pacheco-Valencia , Nodari Vakhania

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

We consider the time-dependent traveling salesman problem (TDTSP), a generalization of the asymmetric traveling salesman problem (ATSP) to incorporate time-dependent cost functions. In our model, the costs of an arc can change arbitrarily…

Optimization and Control · Mathematics 2018-05-04 Christoph Hansknecht , Imke Joormann , Sebastian Stiller

We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…

Data Structures and Algorithms · Computer Science 2015-03-19 Tobias Mömke , Ola Svensson

The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with…

Optimization and Control · Mathematics 2021-09-30 Ulrich Pferschy , Rostislav Stanek

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 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

In the Strip Packing problem (SP), we are given a vertical half-strip $[0,W]\times[0,\infty)$ and a set of $n$ axis-aligned rectangles of width at most $W$. The goal is to find a non-overlapping packing of all rectangles into the strip such…

Data Structures and Algorithms · Computer Science 2022-05-09 Arindam Khan , Aditya Lonkar , Arnab Maiti , Amatya Sharma , Andreas Wiese

Given a metric $(V,d)$ and a $\textsf{root} \in V$, the classic $\textsf{$k$-TSP}$ problem is to find a tour originating at the $\textsf{root}$ of minimum length that visits at least $k$ nodes in $V$. In this work, motivated by applications…

Data Structures and Algorithms · Computer Science 2019-11-07 Haotian Jiang , Jian Li , Daogao Liu , Sahil Singla

TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…

Data Structures and Algorithms · Computer Science 2019-11-12 Yang Li , Junbin Gao , Mingyuan Bai , Chengjun Li , Gang Liu

The Travelling Salesman Problem (TSP), finding a minimal weighted Hamilton cycle in a graph, is a typical problem in operation research and combinatorial optimization. In this paper, based on some novel properties on Hamilton graphs, we…

Discrete Mathematics · Computer Science 2021-04-28 Heping Jiang

Motivated by applications to poaching and burglary prevention, we define a class of weighted Traveling Salesman Problems on metric spaces. The goal is to output an infinite (though typically periodic) tour that visits the n points…

Data Structures and Algorithms · Computer Science 2018-08-03 David Kempe , Mark Klein

The subtour relaxation of the traveling salesman problem (TSP) plays a central role in approximation algorithms and polyhedral studies of the TSP. A long-standing conjecture asserts that the integrality gap of the subtour relaxation for the…

Combinatorics · Mathematics 2026-05-01 William Cook , Stefan Hougardy , Moritz Petrich