# Post travelling salesman problem exponential complexity polynomial

All bounds are given up to a polynomial factor of the input size (poly(n,logM)). (and exponential space for TSP in graphs with bounded .. By posting your answer, you agree to the privacy policy and terms of service.

Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair of The time complexity is much less than O(n!), but still exponential.

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 Yes, but there are exponential number of tours to check! . By posting your answer, you agree to the privacy policy and terms of....

## Post travelling salesman problem exponential complexity polynomial -- journey

Find all posts by Jeff Lichtman. Common Interview Puzzles Interview Experiences.Please green card processes procedures travel documents inquiries germantownalumni.org if you believe this is an error. Find all posts by Indistinguishable. So a matching for the odd degree vertices must be added which increases the order of every odd degree vertex by one. So if you want be famous and win the Gödel prize or better a Turing prize the equivalent to the Nobel in informaticsyou know, only you have to find a polynomial time algorithm that resolve this problem. So my question, is there a better preferable polynomial time algorithm for solving the TSP in a M x N grid? Start here for a quick overview of the site. Find all posts by SmartAlecCat. With arbitrary real coordinates, Euclidean TSP cannot be in such classes, since there are uncountably many possible inputs. And AFAIK, this doesn't always satisfy the triangle inequality e. The decision problem formulation, as mentioned, is "there exists a path of at most cost k that goes through all cities except the starting one exactly. BB code is On. Find all posts by Chronos. Originally Posted by Chronos. Lecture notes in computer science, vol. This also corresponds to the brute force approach described in Vikrams answer.

### Post travelling salesman problem exponential complexity polynomial -- journey

Sci , IEEE Computer Society, pp. One method of doing this was to create a minimum spanning tree of the graph and then double all its edges, which produces the bound that the length of an optimal tour is a most twice the weight of a minimum spanning tree. Publishers - interested in subscribing to the Straight Dope? That version is NP-complete in that it is essentially the same complexity as all other NP-complete decision problems, which, as you point out, can be verified in polynomial time. I fixed my question.