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Las Vegas algorithm; Lock-free and wait-free algorithms; Monte Carlo algorithm; Numerical analysis; Online algorithm; Polynomial time approximation scheme; Problem size; Pseudorandom number generator; Quantum algorithm; Random-restart hill climbing; Randomized algorithm; Running time; Sorting algorithm; Search algorithm; Stable algorithm ...
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. [1]
An algorithm that verifies whether a given subset has sum zero is a verifier. Clearly, summing the integers of a subset can be done in polynomial time, and the subset sum problem is therefore in NP. The above example can be generalized for any decision problem.
A more involved example is the Boom hierarchy of the binary tree, list, bag and set abstract data types. [10] All these data types can be declared by three operations: null , which constructs the empty container, single , which constructs a container from a single element and append , which combines two containers of the same type.
If the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input. An example of a decision problem is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected or not. The formal language ...
For examples of this specification-method applied to the addition algorithm "m+n" see Algorithm examples. An example in Boolos-Burgess-Jeffrey (2002) (pp. 31–32) demonstrates the precision required in a complete specification of an algorithm, in this case to add two numbers: m+n. It is similar to the Stone requirements above.
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 DAA is defined in FIPS PUB 113, [1] which was withdrawn on September 1, 2008.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.
In the field of runtime analysis of algorithms, it is common to specify a computational model in terms of primitive operations allowed which have unit cost, or simply unit-cost operations. A commonly used example is the random-access machine, which has unit cost for read and write access to all of its memory cells. In this respect, it differs ...