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What is the lowest possible average-case time complexity of Shellsort with a deterministic fixed gap sequence? Can 3SUM be solved in strongly sub-quadratic time, that is, in time O(n 2−ϵ) for some ϵ>0? Can the edit distance between two strings of length n be computed in strongly sub-quadratic time?
Moret, B. M. E.; H. D. Shapiro (1991). Algorithms from P to NP, volume 1 - Design and Efficiency . Redwood City, California: Benjamin/Cummings Publishing Company, Inc. Discusses intractability of problems with algorithms having exponential performance in Chapter 2, "Mathematical techniques for the analysis of algorithms."
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman 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 ...
[1] The subset sum problem is a special case of the decision and 0-1 problems where each kind of item, the weight equals the value: =. In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. [2]
Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or −1. The analogous question for matrices with elements equal to 0 or 1 is equivalent since, as will be shown below, the maximal determinant of a {1,−1} matrix of size n is 2 n−1 times the maximal determinant of a {0,1} matrix of size n−1.
In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. [1] [2] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. [3]
Hara, Tani & Yamamoto (2005) claimed the weaker result that unknotting is in AM ∩ co-AM; however, later they retracted this claim. [1] In 2011, Greg Kuperberg proved that (assuming the generalized Riemann hypothesis) the unknotting problem is in co-NP, [2] and in 2016, Marc Lackenby provided an unconditional proof of co-NP membership. [3]