# Questions tagged [traveling-salesman-problem]

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### TSP on a unitary circle

I am interested in knowing which is the expected length of a random path in a circle. That is, if there are $n$ random points located in the unitary circle $\{(x,y): x^2+y^2\leq 1\}$, what is the ...
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### Tour expansion with min-cost flow

Question: has the problem of formulating optimal tour-expansion for Symmetric TSP's already been mentioned as a means for faster tour-expansion in the sense of potentially intergrating more than one ...
25 views

### Degree-constraints for the existence of vertex-disjoint directed cycle covers in digraphs

Given a digraph $G(E,V): (u,v)\in E\implies(v,u)\notin E$, what is known about lower bounds on the indegree and outdegree of the vertices that guarantee the existence of a vertex-disjoint directed ...
88 views

### Could you provide some TSP examples from real world to test a new algorithm?

It's well known that to find a hamilton cycle is NPC, while TSP is NPH. But it seems that for majority of graphs (density of edge > 0.1, order > 100) there is a fast algorithm to find different ...
35 views

### Travelling salesman problem with variable weights

Take a fully connected graph with $v$ vertices. We assign weights to edges using an arbitrary function $f_{ij}(x)$ for pairs of vertices $0 < i, j \le v$, then starting at $c_{0}=0$, traverse the ...
177 views

### Helsgaun's $k$-Opt moves

In his 2009 paper General k-opt submoves for the Lin–Kernighan TSP heuristic, Helsgaun defines the local tour improvements on which the LKH heuristics are based as: several questions arise from that ...
19 views

### Probability that edge exchange yields a tour

let $H$ be a Hamilton cycle in a complete topological symmetric graph $G$ of finite size. Question: what is the probability that a vertex-disjoint cycle cover $C_k$ that is generated from $H$ by ...
42 views

### $\mathrm{LP}$ formulation for $\mathrm{k}$-$\operatorname{opt}$ moves

$\mathrm{k}$-$\operatorname{opt}$ moves are an idea to improve non-optimal Hamilton cycles in weighted symmetric graphs by exchanging $\mathrm{k}$ tour-edges with $\mathrm{k}$ edges that do not belong ...
35 views

### Relation of 1-trees to optimal tours

Question: given a complete symmetric graph $G(V,E)$ with $n$ vertices and edges $e_{ij}$ having weight $\omega_{ij}$, does there always exists a vector of vertex potentials $(\pi_1,\,\dots,\,\pi_n)$ ...