# Question: Is maximum matching NP hard?

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Maximum matching is polynomial-time solvable on normal graphs, see the wikipedia page on matching. Maximum matching is NP-hard in hypergraphs (as shown in this wikipedia page, it is even hard for hypergraphs where each edge contains only 3 vertices).

## Is maximum bipartite matching NP-hard?

Appl. Math. 38, 364–372 (1980; Zbl 0455.05047)] that the problem of finding a maximal matching of minimum size (MMM for short), also called Minimum Edge Dominating Set, is NP-hard in bipartite graphs of maximum degree 3 or planar graphs of maximum degree 3.

## Is maximum matching NP-complete?

Maximum matching with ordering constraints is NP-complete. 2009. 5 p. Abstract A maximum weighted matching in a graph can be computed in polynomial time.

## Is bipartite matching NP-hard?

1 Answer. Unfortunately, this is NP-hard; theres an easy reduction from Set Cover (in fact its arguably just a different way of expressing the same problem).

## Is matching NP-complete?

We show that a restricted form of the perfect matching problem for bipartite graphs is NP-complete. This problem is still NP-complete if the degrees of the vertices are restricted to be 3 or less. For degrees restricted to 2 or less, a polynomial time algorithm exists.

## What does NP-hard stand for?

non-deterministic polynomial-time hardness In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally at least as hard as the hardest problems in NP. A simple example of an NP-hard problem is the subset sum problem.

## What is the difference between NP and NP-complete?

The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in polynomial time .Difference between NP-Hard and NP-Complete:NP-hardNP-CompleteTo solve this problem, do not have to be in NP .To solve this problem, it must be both NP and NP-hard problems.3 more rows•3 Sep 2021

## Are NP problems solvable?

The short answer is that if a problem is in NP, it is indeed solvable.

## Is sorting NP or P?

Sorting Numbers Given a list of numbers, you can verify that whether the list is sorted or not in polynomial time, so the problem is clearly NP. There are known algorithms to sort a list of numbers in polynomial time. (Bubble sort O(n^2) etc. ). Thus the problem is P.

## What is the hardest NP problem?

In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally at least as hard as the hardest problems in NP. A simple example of an NP-hard problem is the subset sum problem.

## Does NP mean Nope?

@Psp: nop/np or nope means no it is used in informal.

## Is NP-complete harder than NP?

The name NP-complete is short for nondeterministic polynomial-time complete. The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC.

## Is traveling salesman NP-hard?

In Chapter 15 we introduced the Traveling Salesman Problem (TSP) and showed that it is NP-hard (Theorem 15.42). The TSP is perhaps the best-studied NP-hard combinatorial optimization problem, and there are many techniques which have been applied.

## What happens if P vs NP is solved?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers problem-solving powers will remain fundamentally and permanently limited.

## Will P vs NP ever be solved?

Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus it is unlikely that natural proofs alone can resolve P = NP.

## Is sorting NP hard?

Pancake flipping is hard - NP hard. French computer scientists have finally proved that sorting pancakes is hard - NP hard.

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