## Can a Travelling Salesman Problem solved in polynomial time?

if the traveling salesman problem can be solved in polynomial time using backtracking then it will become a P . So its false , it cant be solved in polynomial time by deterministic way .

## How do I check my Travelling salesman problem?

To solve the TSP using the Brute-Force approach, you must calculate the total number of routes and then draw and list all the possible routes. Calculate the distance of each route and then choose the shortest one—this is the optimal solution. This method breaks a problem to be solved into several sub-problems.

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Can NP complete problems be solved in polynomial time?

If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

### Has anyone solved the traveling salesman problem?

Scientists in Japan have solved a more complex traveling salesman problem than ever before. The previous standard for instant solving was 16 “cities,” and these scientists have used a new kind of processor to solve 22 cities. They say it would have taken a traditional von Neumann CPU 1,200 years to do the same task.

### What is the Travelling Salesman Problem explain in detail?

The traveling salesman problem (TSP) is an algorithmic problem tasked with finding the shortest route between a set of points and locations that must be visited. Focused on optimization, TSP is often used in computer science to find the most efficient route for data to travel between various nodes.

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What is Travelling salesman problem in DAA?

Traveling-salesman Problem In the traveling salesman Problem, a salesman must visits n cities. We can say that salesman wishes to make a tour or Hamiltonian cycle, visiting each city exactly once and finishing at the city he starts from. There is a non-negative cost c (i, j) to travel from the city i to city j.

## What is Travelling Salesman Problem explain with example?

Is Travelling salesman NP-complete?

Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).

### How do you prove a problem is NP-complete?

Suppose X is solvable in polytime, and let Y be any problem in NP. We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete.

### Which statement is true about traveling salesman problem?

The only known way to verify that a provided solution is the shortest possible solution is to actually solve the entire TSP. Since it takes exponential time to solve NP, the solution cannot be checked in the real polynomial time. Hence, this problem is NP-hard, but not in NP.

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What is Travelling salesman problem is the problem NP complete Justify your answer?

Given a set of cities and the distance between each pair of cities, the travelling salesman problem finds the path between these cities such that it is the shortest path and traverses every city once, returning back to the starting point.