Questions tagged [tsp]

The travelling salesman problem (TSP) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once.

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21 votes
4 answers
2k views

DNA-algorithms and NP-completeness

What is the relationship between DNA-algorithms and the complexity classes defined using Turing machines? What do the complexity measures like time and space correspond to in DNA-algorithms? Can they ...
Aadita Mehra's user avatar
46 votes
4 answers
14k views

Approximation algorithms for Metric TSP

It is known that metric TSP can be approximated within $1.5$ and cannot be approximated better than $123\over 122$ in polynomial time. Is anything known about finding approximation solutions in ...
Alex Golovnev's user avatar
9 votes
2 answers
1k views

Generating interesting combinatorial optimization problems

I'm teaching a course on meta-heuristics and need to generate interesting instances of classic combinatorial problems for the term project. Let's focus on TSP. We are tackling graphs of dimension $200$...
Alejandro Piad's user avatar
12 votes
2 answers
851 views

Euclidean TSP in NP and square root complexity

In this lecture notes by Ola Svensson: http://theory.epfl.ch/osven/courses/Approx13/Notes/lecture4-5.pdf, it is said that we don't know if Euclidean TSP is in NP: The reason being that we do not ...
JS_'s user avatar
  • 363
9 votes
2 answers
7k views

Time complexity of Held-Karp algorithm for TSP

When I looked through "A Dynamic Programming Approach to Sequencing Problems" by Michael Held and Richard M. Karp1, I came up with the following question: why the complexity of their ...
Oleksandr Bondarenko's user avatar
6 votes
3 answers
2k views

A simple approximation algorithm for the TSP

Consider the following extremely simple approximation algorithm for the TSP. Input: A complete weighted graph $G=(V,E).$ Take any three vertices $a,b,c\in V$ and let $H:=(a,b,c,a).$ While there ...
Sacha's user avatar
  • 338
5 votes
1 answer
2k views

Approximation for metric TSP: Worst case using nearest neighbor heuristic?

I'm looking at different heuristics that approximate solutions for a metric Traveling Salesman Problem. I was wondering if there is a worst case ratio of tours calculated by the nearest neighbor ...
Johannes's user avatar
  • 153
4 votes
1 answer
1k views

Heuristics for tsp without triangle inequality

Every heuristic for the traveling salesman problem that I know of (Nearest-Neighbour, Christofides, Held-Karp, ...) assumes that the triangle inequality holds. Are there heuristics to solve the tsp ...
Aerus's user avatar
  • 227