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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."
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? (This is only possible if the strong exponential time hypothesis is false.) Can X + Y sorting be done in o(n 2 log n) time?
The impossibility of the case A = 1 or B = 1 is implied by Catalan's conjecture, proven in 2002 by Preda Mihăilescu. (Notice C cannot be 1, or one of A and B must be 0, which is not permitted.) A potential class of solutions to the equation, namely those with A, B, C also forming a Pythagorean triple, were considered by L. Jesmanowicz in the ...
In most cases, the distance between two nodes in the TSP network is the same in both directions. The case where the distance from A to B is not equal to the distance from B to A is called asymmetric TSP. A practical application of an asymmetric TSP is route optimization using street-level routing (which is made asymmetric by one-way streets ...
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]
Burnside considered some easy cases in his original paper: B(1, n) is the cyclic group of order n. B(m, 2) is the direct product of m copies of the cyclic group of order 2 and hence finite. [note 1] The following additional results are known (Burnside, Sanov, M. Hall): B(m, 3), B(m, 4), and B(m, 6) are finite for all m.
The expression problem is a challenging problem in programming languages that concerns the extensibility and modularity of statically typed data abstractions. The goal is to define a data abstraction that is extensible both in its representations and its behaviors, where one can add new representations and new behaviors to the data abstraction, without recompiling existing code, and while ...
For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2; for 2 2 a + 1 there is only 1 increase as 1 rises to 2 and falls to 1 so the result is 3a + 1. When b is 2 k − 1 then there will be k rises and the result will be 3 k a + 3 k − 1.