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We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and…

Data Structures and Algorithms · Computer Science 2009-10-06 Michel X. Goemans

We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…

Optimization and Control · Mathematics 2021-01-21 Simone Cacace , Anna Chiara Lai , Paola Loreti

A lower bound on the solution to the traveling salesman problem is provided, which is expressed in terms of eigenvalues related to the distance matrix for the problem. This bound has many interesting properties such as transforming…

Combinatorics · Mathematics 2025-09-24 Lasse H. Wolff

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

Discrete Mathematics · Computer Science 2012-02-06 Harold Connamacher , Michael Molloy

Recent work on optimization problems in random link models has verified several conjectures originating in statistical physics and the replica and cavity methods. In particular the numerical value 2.0415 for the limit length of a traveling…

Probability · Mathematics 2018-01-09 Giorgio Parisi , Johan Wästlund

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

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor…

Data Structures and Algorithms · Computer Science 2017-09-05 Ola Svensson , Jakub Tarnawski , László A. Végh

Facet-defining inequalities of the symmetric Traveling Salesman Problem (TSP) polytope play a prominent role in both polyhedral TSP research and state-of-the-art TSP solvers. In this paper, we introduce a new class of facet-defining…

Combinatorics · Mathematics 2020-12-24 Samuel C. Gutekunst , David P. Williamson

The Traveling Salesman Problem (TSP) in the $d$-dimensional Euclidean space is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial…

Data Structures and Algorithms · Computer Science 2025-04-07 Tobias Mömke , Hang Zhou

STSP seeks a pair of pickup and delivery tours in two distinct networks, where the two tours are related by LIFO contraints. We address here the problem approximability. We notably establish that asymmetric MaxSTSP and MinSTSP12 are APX,…

Computational Complexity · Computer Science 2010-09-28 Sophie Toulouse

We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We…

Quantum Physics · Physics 2007-05-23 Debabrata Goswami , Harish Karnick , Prateek Jain , Hemanta K. Maji

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

With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…

Artificial Intelligence · Computer Science 2017-05-26 Yihui He , Ming Xiang

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…

Discrete Mathematics · Computer Science 2015-07-17 Binay Bhattacharya , Ante Ćustić , Akbar Rafiey , Arash Rafiey , Vladyslav Sokol

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 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

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck…

Data Structures and Algorithms · Computer Science 2020-12-29 Hyung-Chan An , Robert Kleinberg , David B. Shmoys

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

This paper describes TSP exact solution of polynomial complexity. It is considered properties of proposed method. Effectiveness of proposed solution is illustrated by outcomes of computer modeling.

Computational Complexity · Computer Science 2007-05-23 Vadim Yatsenko

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