Related papers: Colored Points Traveling Salesman Problem
The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide…
The multiple Traveling Salesmen Problem (mTSP) is a general extension of the famous NP-hard Traveling Salesmen Problem (TSP), that there are m (m > 1) salesmen to visit the cities. In this paper, we address the mTSP with both the minsum…
We study a problem proposed by Hurtado et al. (2016) motivated by sparse set visualization. Given $n$ points in the plane, each labeled with one or more primary colors, a \emph{colored spanning graph} (CSG) is a graph such that for each…
This study addresses the Min-Max Multiple Traveling Salesmen Problem ($m^3$-TSP), which aims to coordinate tours for multiple salesmen such that the length of the longest tour is minimized. Due to its NP-hard nature, exact solvers become…
In the Traveling Salesperson Problem (TSP) we are given a list of locations and the distances between each pair of them. The goal is to find the shortest possible tour that visits each location exactly once and returns to the starting…
We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP…
We provide a new upper bound for traveling salesman problem (TSP) in cubic graphs, i.e. graphs with maximum vertex degree three, and prove that the problem for an $n$-vertex graph can be solved in $O(1.2553^n)$ time and in linear space. We…
This paper introduces a novel edge-based encoding technique for solving the Traveling Salesman Problem (TSP) on a quantum computer, reducing the required number of qubits. For implementation in real quantum devices, we applied the subspace…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
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…
This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…
The Graphical Traveling Salesperson Problem (GTSP) is the problem of assigning, for a given weighted graph, a nonnegative number $x_e$ each edge $e$ such that the induced multi-subgraph is of minimum weight among those that are spanning,…
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…
Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number…
In this paper, we study problems of connecting classes of points via noncrossing structures. Given a set of colored terminal points, we want to find a graph for each color that connects all terminals of its color with the restriction that…
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…
This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformulations that approximate the Euclidean distances and…