# What are tractable and intractable problems?

## What are tractable and intractable problems?

Tractable Problem: a problem that is solvable by a polynomial-time algorithm. The upper bound is polynomial. Intractable Problem: a problem that cannot be solved by a polynomial-time al- gorithm.

## What is the difference between Undecidable and intractable problems?

Undecidable problems are those for which no computer solution can ever exist, while intractable problems are those for which there is strong evidence that, although they can be solved by a computer, they cannot be solved sufficiently fast that the solution is truly useful in practice.

What is an intractable problem?

From a computational complexity stance, intractable problems are problems for which there exist no efficient algorithms to solve them. Most intractable problems have an algorithm – the same algorithm – that provides a solution, and that algorithm is the brute-force search.

### Is the Travelling salesman problem tractable?

As the only solutions to TSP are intractable, TSP is known as an intractable problem. It hasn’t actually been proven that there is no tractable solution to TSP, although many of the world’s top computer scientists have worked on this problem for the last 40 years, trying to find a solution but without success.

### What are the tractable and non tractable problem?

computational complexity Algorithms for solving hard, or intractable, problems, on… …said to be easy, or tractable. A problem is called NP if its solution can be guessed and verified in polynomial time, and nondeterministic means that no particular rule is followed to make the guess.

What is a tractable model?

1. A ‘tractable’ model is one that you can solve, which means there are several types of tractability : analytical tractability (finding a solution to a theoretical model), empirical tractability (being able to estimate/calibrate your model) and computational tractability (finding numerical solutions).

#### Which of the following are examples of intractable problems?

10.3 Examples of some Intractable Problems

• 10.3.1 Traveling Salesman Problem.
• 10.3.2 Subset Sum.
• 10.3.3 Knapsack Problem.
• 10.3.4 Bin Packing.
• 10.3.5 Job Shop Scheduling.
• 10.3.6 Satisfiability.

#### How does the practical Travelling salesman problem differ from the classical Travelling salesman problem?

The Travelling Salesman Problem involves finding a tour of minimum total weight. In the classical problem, each vertex must be visited exactly once before returning to the start. In the practical problem, each vertex must be visited at least once before returning to the start.

What is tractable decision problem?

Tractable problem, in computational complexity theory, a problem that can be solved in polynomial time. Tractable, ease of obtaining a mathematical solution such as a closed-form expression.

## What is the difference between P and NP problems?

P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].