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This article is a list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known or when experts in the field disagree about proposed solutions.
In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard , so it cannot be solved by a polynomial-time algorithm if P ≠ NP . Moreover, it is hard to approximate – it cannot be approximated up to a factor smaller than 2 if the unique games conjecture is true.
The quadratic fit suggests that the algorithmic complexity of the problem is O((log(n)) 2). [1] All of the above discussion has assumed that P means "easy" and "not in P" means "difficult", an assumption known as Cobham's thesis. It is a common assumption in complexity theory; but there are caveats. First, it can be false in practice.
There are various kinds of covering problems in graph theory, computational geometry and more; see Category:Covering problems. Other stochastic related versions of the problem can be found. [2] The covering problem of Rado, where a series of squares with parallel edges needs to cover an area of 1. For any set meeting these conditions, a subset ...
NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. [2] [Note 1]
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
For example, it's quite possible to reduce a difficult-to-solve NP-complete problem like the boolean satisfiability problem to a trivial problem, like determining if a number equals zero, by having the reduction machine solve the problem in exponential time and output zero only if there is a solution. However, this does not achieve much ...