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Questions tagged [traveling-salesman]

The Traveling Salesman Problem and variants

The Traveling Salesman Problem (also spelled Travelling Salesman Problem, or TSP for short) asks, given a weighted graph, what is the lowest-weight cycle that visits each node exactly once. The decision problem of determining whether such a cycle exists under a given maximum weight is also known as TSP.

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How can I verify a solution to Travelling Salesman Problem in polynomial time?

So, TSP (Travelling salesman problem) decision problem is NP complete. But I do not understand how I can verify that a given solution to TSP is in fact optimal in polynomial time, given that there is no way to find the optimal solution in polynomial…
Lazer
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How is the traveling salesman problem verifiable in polynomial time?

So I understand the idea that the decision problem is defined as Is there a path P such that the cost is lower than C? and you can easily check this is true by verifying a path you receive. However, what if there is no path that fits this…
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If I can solve Sudoku, can I solve the Travelling Salesman Problem (TSP)? If so, how?

Let us say there is a program such that if you give a partially filled Sudoku of any size it gives you corresponding completed Sudoku. Can you treat this program as a black box and use this to solve TSP? I mean is there a way to represent TSP…
user101371
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What is the optimal solution of the 1962 Procter and Gamble's TSP Contest?

In 1962, you could win a prize of \$ 10 000 (about \$ 80 000 in today's money) if you found the solution to an Euclidean travelling salesman problem defined on 33 cities. http://www.math.uwaterloo.ca/tsp/history/pictorial/car54.html Looking at the…
Martin Drozdik
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Traveling Salesman Problem with Neural Network

I was curious if there were any new developments in solving the traveling salesman problem using something like a Hopfield recurrent neural network. I feel like I saw something about recent research getting a breakthrough in this, but I can't find…
Rob
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Known facets of the Travelling Salesman Problem polytope

For the branch-and-cut method, it is essential to know many facets of the polytopes generated by the problem. However, it is currently one of the hardest problems to actually calculate all facets of such polytopes as they rapidly grow in size. For…
stefan
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How can the shortest traveling salesman tour be found in $O(2^n poly(n))$ time and less than exponential space?

I'm stuck on problem 9.4 from The Nature of Computation which reads: Dynamic Salesman. A naive search algorithm for TSP takes $O(n!)$ time to check all tours. Use dynamic programming to reduce this to a simple exponential, i.e., to solve TSP in…
Sebastian Oberhoff
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Why the need for TSP solvers when there are SAT solvers?

Concorde TSP is a solver for TSP. SAT solvers are solvers for boolean satisfiability. TSP and SAT are NP-complete. Hence, why spent the time to develop Concorde TSP when there is an abundance of SAT solvers in the market back then?
Jessica Cage
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Why does TSP require no repetition of cities?

It seems odd to me that the TSP denies the possibility of repeated cities. The goal of this traveling salesman is to go as fast as possible and visit all of the cities, right? So what if it is faster to travel through a city you have already been…
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Why does this graph show the tightness of MST heuristic's 2-approximation bound?

This is a homework problem I've been given and I've been raking my brain for hours (so I'm satisfied with some pointers). I know already that the approximation ratio cannot be worse than $2$. I have a wheel graph, where each edge has cost $1$ and…
oarfish
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Minimum distance between start and end by going through must visit points in a maze

So, suppose i have a maze, which has a start point and an end point, marked with Orange and red respectively and my goal is to find the minimum distance between them. The blocked path is represented by black colour and the open path is represented…
zero infinity
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How does the 3-opt algorithm for TSP work?

I understand that the 3-Opt Heuristic for solving the Traveling Salesman problem involves removing three edges from a graph and adding three more to recomplete the tour. However, I've seen many papers that mention that when three edges are removed,…
u3l
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NP-hardness of a special traveling salesman problem

Consider we have $n$ vertices, $v_1,\ldots,v_n$. We have two positive values $(a_i,b_i)$ associated with each $v_i$. The edge weight $w(v_iv_j)=a_ia_j+b_ib_j$. Is it NP-hard to solve the traveling salesman problem on this graph? In the special case…
Chao Xu
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Does there exist a travelling salesmen generating algorithm?

I'm curious if somebody has already figured this out. Is there an efficient algorithm that will generate (in $\mathbb{R}^2$) a sequence of points in such a way that the solution to the travelling salesmen problem is known a priori, and such that we…
JoeTheShmoe
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Traveling Salesman -- number of qubits required?

I'm trying (in vain) to get a beginner's grasp of quantum computing, so doing a lot of reading. I've started looking at IBM's QISkit Jupyter Notebooks, and came across the one on MaxCut problems. In there, they give an example of how you could use…
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