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Many algorithms with bad worst-case performance have good average-case performance. For problems we want to solve, this is a good thing: we can hope that the particular instances we care about are average. For cryptography, this is very bad: we want typical instances of a cryptographic problem to be hard.
In computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process.
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures.
From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [8] [9] [10] In fact, Dijkstra's explanation of the logic behind the algorithm, [11] namely Problem 2.
Since algorithms are platform-independent (i.e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system), there are additional significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.
Given two sets, A and T, together with a weight function C : A × T → R. Find a bijection f : A → T such that the cost function: (, ()) is minimized. Usually the weight function is viewed as a square real-valued matrix C, so that the cost function is written down as:
The Data Authentication Algorithm (DAA) is a former U.S. government standard for producing cryptographic message authentication codes. DAA is defined in FIPS PUB 113, [1] which was withdrawn on September 1, 2008. [citation needed] The algorithm is not considered secure by today's standards.