English
Related papers

Related papers: Approximating Graphic TSP by Matchings

200 papers

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

We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower…

Discrete Mathematics · Computer Science 2018-08-29 András Sebő , Anke van Zuylen

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

We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning…

Data Structures and Algorithms · Computer Science 2020-12-14 J. Cheriyan , R. Cummings , J. Dippel , J. Zhu

Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…

Data Structures and Algorithms · Computer Science 2010-09-01 Nikhil Bansal , Anupam Gupta , Jian Li , Julian Mestre , Viswanath Nagarajan , Atri Rudra

The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…

Data Structures and Algorithms · Computer Science 2022-08-25 Etienne Bamas , Marina Drygala , Ola Svensson

The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph…

Artificial Intelligence · Computer Science 2020-07-10 Amal Nammouchi , Hakim Ghazzai , Yehia Massoud

We prove explicit approximation hardness results for the Graphic TSP on cubic and subcubic graphs as well as the new inapproximability bounds for the corresponding instances of the (1,2)-TSP. The proof technique uses new modular…

Computational Complexity · Computer Science 2013-05-15 Marek Karpinski , Richard Schmied

In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…

Data Structures and Algorithms · Computer Science 2020-12-23 Katarzyna Paluch

Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…

Discrete Mathematics · Computer Science 2021-08-19 Arash Haddadan , Alantha Newman

For the traveling salesman problem (TSP), the existing supervised learning based algorithms suffer seriously from the lack of generalization ability. To overcome this drawback, this paper tries to train (in supervised manner) a small-scale…

Machine Learning · Computer Science 2021-02-25 Zhang-Hua Fu , Kai-Bin Qiu , Hongyuan Zha

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

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

We introduce a topological feedback mechanism for the Travelling Salesman Problem (TSP) by analyzing the divergence between a tour and the minimum spanning tree (MST). Our key contribution is a canonical decomposition theorem that expresses…

Computational Geometry · Computer Science 2025-12-19 Ilya Trofimov , Daria Voronkova , Alexander Mironenko , Anton Dmitriev , Eduard Tulchinskii , Evgeny Burnaev , Serguei Barannikov

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

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

This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach…

Machine Learning · Statistics 2024-08-12 Ernesto Araya Valdivia , Hemant Tyagi

Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of the…

Optimization and Control · Mathematics 2025-12-08 Toshiaki Yamanaka

In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…

Data Structures and Algorithms · Computer Science 2014-01-16 Katarzyna Paluch

The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space $(V,d)$ with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V.…

Data Structures and Algorithms · Computer Science 2015-01-07 Zachary Friggstad , Anupam Gupta , Mohit Singh