FAQs
A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means "at least as hard as any NP-problem," although it might, in fact, be harder.
Does NP-hard mean unsolvable? ›
Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are provably not NP-hard (unless P=NP).
Has an NP-hard problem ever been solved? ›
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
What is an example of a NP problem? ›
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
Is chess NP-hard? ›
Is Chess NP complete or NP hard? “Real” chess is in P because it's of finite size so all positions can be (in a theoretical, computational-complexity sense) looked up in a table. “Generalized” chess is harder than NP, but you have to define how you generalize it to larger boards.
How to prove that a problem is NP-hard? ›
To prove that problem A is NP-hard, reduce a known NP-hard problem to A. In other words, to prove that your problem is hard, you need to describe an efficient algorithm to solve a different problem, which you already know is hard, using an hypothetical efficient algorithm for your problem as a black-box subroutine.
Can humans solve NP-hard problems? ›
NP-hard problems commonly come up as human-solvable puzzles. Like Sudoku... or perhaps a more applicable problem... layout and routing of electronic components on a PCB and/or chip. Or even assembly-language register allocation (coloring and packing problem).
Is sudoku NP? ›
It is generally known that the sudoku problem is NP-complete [11].
Can an AP problem be NP-hard? ›
A problem is NP-hard if an algorithm for its solution can be modified to solve any NP problem—or any P problem, for that matter, as P problems are a subset of NP problems. (Not all NP-hard problems are members of the class of NP problems, however.)
Can AI solve P vs NP? ›
AI, with its advanced pattern recognition and data processing capabilities, is ideally positioned to tackle the P vs NP problem. Machine learning algorithms can process and analyze vast datasets much faster than humans, identifying patterns that could lead to a solution.
So, a quantum computer with bounded error can solve all types of problems in P and BPP in polynomial time. It can solve some NP types of problems in polynomial time, with factoring via Shor's algorithm serving as the most popular example.
How do you deal with hard NP problems? ›
Overcoming Challenges While Solving NP Hard Problems
- Using heuristic or approximation algorithms that find near-optimal solutions much more efficiently than exhaustive search.
- Applying more computational resources, either through parallelization or by using more powerful hardware.
Some well-known games that can be proven to be NP-hard (in some form or other) include Tetris, Minesweeper, Checkers, Chess, Dots and boxes.
Is traveling salesman NP-hard? ›
The travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in ...
Can NP problems be solved by a computer? ›
Computers can easily check solutions to NP problems, but devising an algorithm that can propose solutions to NP problems in a reasonable time is much more difficult. That's what makes NP more interesting!
What does NP stand for? ›
abbreviation for
Informal. ( used in digital communications) no problem. Also np. noun phrase. nurse-practitioner.
Is tsp NP-hard or NP-complete? ›
The TSP is perhaps the best-studied NP-hard combinatorial optimization problem, and there are many techniques which have been applied.
What is an NP-hard language? ›
Def 2.2 A language L is NP-hard if for every language L0 ∈ NP, there is a reduction from L0 to L. A language L is NP-complete if it is NP-hard and also L ∈ NP. We remark that one could also define NP-hardness via Cook reductions. However, this seems to lead to a different definition.
Are NP-hard problems harder than NP-complete? ›
There's also an upper bound to “how hard” an NP problem can be. This set of “most difficult” NP programs (which again, might just be P) form the NP-complete complexity class. There are also problems that can't even be verified in polynomial time. NP-hard is the set of all problems that are NP-complete or harder.
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