# Questions tagged [traveling-salesman-problem]

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### Mathematical problems reducing to the traveling salesman problem

The superpermutation problem is: what is the shortest word that contains every permutation of $k$ letters as a substring. This can phrased as a Travelling Salesman Problem, where the nodes of your ...
34 views

### Transformation of asymmetric traveling salesman problems into Chinese postman problems

I have found transformations of Chinese Postman Problems (CPPs) into Asymmetric Traveling Salesman Problems (ATSPs), but didn't find anything about transformations in the opposite direction. Having ...
322 views

### Traveling Salesman Problem on finite group

Given a finite group $H$, define a norm on $H$ to be a function $f : H \rightarrow \mathbb{R}_{\geq 0}$ satisfying: $f(x) = 0 \iff x = e$ is the identity; $\forall x \in H$, we have $f(x) = f(x^{-1})$...
157 views

Euclidian (planar) TSP asks for a tour with the minimum total length. The problem is known to be NP-hard. I am interested in the variant of finding a closed tour with the minimum enclosed area (...
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### What would $\mathcal{P} \neq \mathcal{NP}$ tell us about some non-constructive proofs?

Let me sum up my - hopefully correct - understanding of the travelling salesman problem and complexity classes. It's about decision problems: "[...] a decision problem is a problem that can be ...
126 views

### Description of Linear Time Algorithm for TSP in Halin Graphs

I am looking for a description of the linear time algorithm for the TSP in Halin graphs, that was given in "G. Cornuejols, D. Naddef, and W.R. Pulleyblank. Halin graphs and the travelling ...
102 views

### Hamiltonian cycle polytope for the hypercube graph

Let $Q_n$ denote the $n$ dimensional hypercube graph (i.e., graph formed from the vertices and edges of an n-dimensional hypercube). Denote the set of edges and vertices of $Q_n$ by $E_n$ and $V_n$ ...
115 views

### Corporate salesman problem

A salesman is employed by a large corporation. He has a $n$ cities to visit, connected by roads, forming a graph. But as travel takes a lot of time, he has to pick hotels between visits. He cannot ...
966 views

### Is there a lower bound for the computational complexity of the traveling salesman problem?

A (non-mathematician) acquaintance of mine recently proposed to me a polynomial-time algorithm for solving the traveling salesman problem. While I was able to point out a flaw in his approach, it did ...
Suppose I have n sets $X_1,\dots,X_n$ consisting of $k$ points each, where all $nk$ points are i.i.d. uniform random samples in the unit square $[0,1]\times[0,1]$. Consider the shortest path that ...